The Dynamics of Heat

Hans U. Fuchs

Chapter 1 Hotness, Heat, and Energy - all with Video Answers

Educators

Chapter Questions

Problem 1

In what sense is hotness the intensity of heat? Why do we have to distinguish it from quantities of heat? To what other quantities in physics may the intensity of heat be compared?

Jerrah Biggerstaff

Numerade Educator

04:43

Consider a moving body that splits into two halves which continue moving along together. Which mechanical quantity is divided among the bodies? Which other mechanical variable is not divided up, leaving each of the parts with its initial value? Compare electrical and thermal phenomena to this mechanical example. Which electrical or thermal quantities correspond to the mechanical variables?

Ajay Singhal

Numerade Educator

01:29

Problem 3

List everyday phenomena which are responsible for our intuitive notion of heat content of bodies. Can you turn the qualitative idea into a physical quantity having a precise meaning?

Shelby Mohamed

Numerade Educator

01:04

Problem 4

Why shouldn't we think of energy as a mechanical, electrical or thermal quantity? Why would it be particularly wrong to identify stored energy as mechanical, electrical, thermal or other? What consequence does this have for identifying "heat" as stored energy?

Ma Ednelyn Lim

Numerade Educator

01:01

Problem 5

What happens to all bodies under all circumstances if their energy is increased? Which physical quantity changes if this happens? What kind of conclusions cannot be drawn from the statement that the energy of a body has changed?

Narayan Hari

Numerade Educator

01:52

Problem 6

With the help of physical quantities, explain the difference between making a body rotate and making it warmer.

Prabhu Ramji

Numerade Educator

08:54

Problem 7

Which interpretation of "heat" comes close to Carnot's image that heat can do work? How did Carnot compare heat to other quantities?

Yaqub Khan

Numerade Educator

03:06

Problem 8

Compare different substancelike physical quantities such as momentum, charge, amount of substance, and entropy. Which two properties do they all have in common? What are possible differences between the quantities listed?

Supratim Pal

Numerade Educator

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Problem 9

Consider a box containing water and an immersion heater (Figure 41). Except for the electrical wires leading to the heater, the system is totally insulated from the environment. Let the heater make the water hotter. If you take the entire setup as the system, why would it be wrong to say that the system has been heated? (Remember the definition of heating, or cooling, in Section 1.1.3.) What does this mean with respect to the question of where the heat has come from which has made the water warmer? What is heat in this case?
FIGURE 41 can't copy. Problem 9.

David Collins

Numerade Educator

01:31

Problem 10

Rephrase the following expressions in terms of entropy. In which cases would reference to energy be clearly wrong? Do any of the terms and expressions have nothing to do with entropy?
a) heat engine, heat pump; b) heat exchanger; c) heating and cooling; d) heat flow, transfer of heat; e) convective heat flow; f) heat source; g) storage of heat, heat reservoir; h) phenomena in which heat causes motion; i) solar heater; j) production of heat; $k$ ) heat transfer coefficient; l) pumping heat from the cold enclosure; k) heating power.

Shubham Kanungo

Numerade Educator

01:07

Problem 11

An electrical resistor element $R_x$ is used as a thermometer. It is placed as one of the four resistors in a circuit (Figure 42). There is no current through the galvanometer (G) if the thermometer is put in water with a temperature of $20^{\circ} \mathrm{C}$ and the resistor $R_s$ is given a value of $10.0 \mathrm{k} \Omega$ Now we place the thermometer into a different fluid. Again, electricity does not flow through the galvanometer if we increase $R_s$ by 1000 $\Omega$ What is the temperature of the second fluid? The coefficient of temperature of the platinum resistor is $2.0 \cdot 10^{-3} \mathrm{~K}^{-1}$.
FIGURE 42 can't copy. Problem 11.

Prabhu Ramji

Numerade Educator

07:56

Problem 12

Water in a cylinder fitted with a piston is evaporated completely by heating at constant pressure. (The piston is moved to compensate for the increase of volume.) In a second step the steam is heated further at constant volume. Finally, an adiabatic expansion decreases the temperature below the initial value at which vaporization took place (without condensation).
a) Sketch the steps in a $T-S$ diagram. b) Prepare a rough sketch of the operations in a $T-V$ diagram. c) What kind of process can bring the entropy content of the fluid back to its initial value? d) Can you think of a single operation from the list of processes discussed in Section 1.3 which would take the fluid back to its original state?

Vipender Yadav

Numerade Educator

00:44

Problem 13

Do any of the simple processes discussed in Section 1.3 lead from the lower right to the upper left corner of the T-S diagram? Could any two achieve the goal of changing a fluid's state in such a manner? Will your answer be different for air and for water in a range of temperatures including the latter's anomaly?

David Collins

Numerade Educator

01:40

Problem 14

Phenomena in which heat causes motion, i.e. thermomechanical processes, are probably the most conspicuous ones involving the action of heat. Do you know of electrical, chemical, or other phenomena which are caused by thermal processes?

Jacob Paiste

Numerade Educator

04:35

Problem 15

How large must the entropy current through an ideal Carnot engine be if its power is 10 kW , and the upper and the lower operating temperatures are $500^{\circ} \mathrm{C}$ and $100^{\circ} \mathrm{C}$, respectively? How does your answer change if you double the power? If you double the temperature difference?

Supratim Pal

Numerade Educator

02:45

Problem 16

A large power plant of 1.0 GW electrical power emits a thermal energy current to the environment twice as large as the useful one. At what rate does the environment, which has a temperature of $25^{\circ} \mathrm{C}$, receive entropy?

Averell Hause

Carnegie Mellon University

01:31

Problem 17

An immersion heater has a temperature of $120^{\circ} \mathrm{C}$ as it emits an energy current equal to 0.80 kW . a) How large is the current of entropy flowing across the surface of the heater? b) If the temperature of the water receiving the heat is equal to $80^{\circ} \mathrm{C}$, how much entropy flows into the water?

Manik Pulyani

Numerade Educator

02:01

Problem 18

Sunlight falling on a window is partly reflected ( $10 \%$ ) and mostly transmitted $(87 \%)$. The rest is absorbed evenly throughout the glass. The energy current associated with the radiation is equal to 900 W . If the temperature of the glass is equal to $30^{\circ} \mathrm{C}$, how large is the rate at which entropy is received by this body?

Vipender Yadav

Numerade Educator

01:43

Problem 19

In cooling, a body of uniform temperature emits currents of entropy and energy equal to $100 \mathrm{~W} / \mathrm{K}$ and $6.0 \cdot 10^4 \mathrm{~W}$, respectively. What is the temperature of the body?

Penny Riley

Numerade Educator

04:59

Problem 20

As a body is heated, its current of entropy increases linearly from $20 \mathrm{~W} / \mathrm{K}$ to $40 \mathrm{~W} /$ K in 100 s , and its temperature goes from $100^{\circ} \mathrm{C}$ to $70^{\circ} \mathrm{C}$ (also linearly). a) Calculate the thermal energy current received by the body as a function of time. b) How much entropy and energy have been absorbed by the body during the process? c) Is this scenario physically possible? Can a body get colder as it receives heat without losing any?

Eduard Sanchez

Numerade Educator

03:18

Problem 21

A mixture of water and ice is heated in such a way that ice melts at a rate of 0.020 $\mathrm{kg} / \mathrm{min}$. a) How large is the current of entropy absorbed by the mixture? b) How much energy does the mixture receive after 10 minutes of heating?

Ma Ednelyn Lim

Numerade Educator

01:19

Problem 22

It is common to tabulate and use amounts of energy transferred in heating for the melting or the vaporization of bodies. These quantities, referred to unit mass, are called the specific enthalpy of fusion $(q)$ and the specific enthalpy of vaporization $(r)$, respectively. What is the relationship between $q$ and $r$ and the molar latent entropies of fusion and of vaporization? (See Tables A. 4 and A.5.)

Lottie Adams

Numerade Educator

02:44

Problem 23

A Carnot heat engine employing air in a closed cylinder fitted with a piston does not exchange energy at a constant rate during its four-stage cycle. In what sense, then, should we understand Equation (11)? Can you write the equivalent statement integrated over one full cycle?

Sanjeev Kumar

Numerade Educator

10:51

Problem 24

Two or more ideal Carnot heat engines operate in sequence, which means that the entropy rejected by one engine is used by the following one. Each of the engines runs in a distinct interval of temperatures between $T_{\max }$ and $T_{\min }$, with the intervals seamlessly covering the entire range of temperatures. a) Show that the power of the sequence of engines is equal to the power of a single engine running between $T_{\max }$ and $T_{\text {min }}$. b) Allow for entropy to be added or withdrawn at each inlet to an engine. Show that in this case the power of the sequence of devices should be equal to

$$
\begin{aligned}
& P=\sum_{i=1}^N I_s\left(T_i\right) \Delta T_i \\
& \Delta T_i=T_i-T_{i+1} \quad, \quad T_1=T_{\max } \quad, \quad T_{N+1}=T_{\min }
\end{aligned}
$$

c) If the entropy current is a continuous function of temperature (between the maximum and the minimum values), show that the power should be calculated according to

$$
P=\int_{T_{\max }}^{T_{\min }} I_s(T) d T
$$

Henrique Saito

Numerade Educator

01:47

Problem 25

How can we infer an absolute temperature scale by measuring the efficiency of an ideal heat engine?

Mahnoor Amin

Numerade Educator

04:45

Problem 26

Would you treat solar radiation as a high or a low temperature heat source? Discuss the implications of your decision.

Keshav Singh

Numerade Educator

04:06

Problem 27

The $C O P$ of a refrigerator is defined as the ratio of the thermal energy current extracted from the cold body and the power needed to drive the engine.
a) Derive the formula for the $C O P$, and calculate the value for an ideal refrigerator operating between temperatures of $-20^{\circ} \mathrm{C}$ and $25^{\circ} \mathrm{C}$. b) Explain the difference in the viewpoints taken for heat pumps and refrigerators.

Averell Hause

Carnegie Mellon University

01:21

Problem 28

If the entropy flowing conductively through the metal bar in Example 21 had been allowed to drive an ideal Carnot engine, how large would its mechanical power be? Since no energy has been released for mechanical purposes in conduction, this power is lost. Prove that the loss of power is equal to the product of the rate of production of entropy in the bar and the temperature of the colder end.

Manik Pulyani

Numerade Educator

02:31

Problem 29

A mixture of ice and water is placed in a freezer having a constant interior temperature of $-18^{\circ} \mathrm{C}$. If the refrigerator works as an ideal Carnot engine, what is the power needed for its operation? Ice is to be formed at a rate of 10 g per minute. The temperature of the environment is taken to be $22^{\circ} \mathrm{C}$. What is the difference between this problem and Example 17?

Manish Jain

Numerade Educator

01:35

Problem 30

Because of imperfect insulation, a thermal energy current of 10 W passes through the walls of the freezer in the previous problem. Answer the questions of Problem 29 for the new situation.

Manish Jain

Numerade Educator

04:16

Problem 31

In a single stroke of a bicycle pump, air is compressed very rapidly. Compare reversible and dissipative compression. In a dissipative process, would the volume be larger, equal, or smaller than the one found in reversible operation for equal final temperatures? At equal final volume, would the temperature be larger, equal, or smaller in the dissipative case than in the reversible one?

Khoobchandra Agrawal

Numerade Educator

15:00

Problem 32

Consider the law of balance of entropy and the quantities introduced in this context.
a) Can you give a formal definition of entropy absorbed and entropy emitted in terms of integrals of the flux of entropy? Use the definitions to show that the entropy exchanged equals the entropy absorbed minus the entropy emitted. b) Write down the formal definition of an amount of entropy generated; see Equation (33).

Ravindra Yadav

Numerade Educator

03:58

Problem 33

Over a time span of 100 s , the entropy of a body increases linearly from $300 \mathrm{~J} / \mathrm{K}$ to $500 \mathrm{~J} / \mathrm{K}$. At the same time the rate of generation of entropy decreases from $5 \mathrm{~W} / \mathrm{K}$ to zero.
a) Compute the net flux of entropy as a function of time. b) How much entropy is exchanged, and absorbed, and emitted?

Amit Srivastava

Numerade Educator

03:18

Problem 34

A mixture of ice and water is heated as in Problem 21. a) Calculate the rate of change of entropy of the mixture. c) How large is the rate of change of energy of the volume? Why is it not precisely equal to the energy current in heating?

Ma Ednelyn Lim

Numerade Educator

01:10

Problem 35

Consider two solid bodies at equal temperatures in thermal contact and completely isolated from the surroundings. What would have to happen if one of the bodies were to get hotter at the expense of the other? Is it possible at all to make one body hotter while the other is cooled?

Joseph Fritchman

Numerade Educator

00:37

Problem 36

Consider two bodies in thermal contact. Their temperatures are different, which causes entropy to flow from the hotter to the cooler system. Is it possible to set up a model of the process for which the temperatures of each of the two bodies are uniform? Where is entropy produced?

Vipender Yadav

Numerade Educator

01:31

Problem 37

Consider water being heated by an immersion heater. a) If you consider the body of water as a system, what is its equation of balance of entropy? (Assume the distribution of entropy through the system to take place reversibly; what does this mean for the conduction of entropy through the system?) b) Answer the question for the case in which you take the system to be made up of water plus heating coil.

Manik Pulyani

Numerade Educator

02:04

Problem 38

Usually, the energy added in heating is called "heat." How much "heat" is added in stirring water with a paddle wheel? What happens to the temperature of the water?

Dading Chen

Numerade Educator

02:25

Problem 39

If the isothermal expansion or compression of air is dissipative, is the energy exchanged in heating still equal to the area under the isotherm in the $T-S$ diagram? Is there a difference in your answers for compression and expansion?

Shahab Ullah

Numerade Educator

04:00

Problem 40

Allow for dissipation in the engines of the heating scheme $B$ of Example 18. Assume the temperature of the water to be distinct from the temperatures of both the furnace and the environment. The heat engine and the heat pump are actually running. Is it possible for dissipation to be so large that the ratio of heating power to solar power becomes equal to 1 , or even less than 1 ?

Shoukat Ali

Other Schools

01:21

Problem 41

Derive the rate of production of entropy for heat transfer which obeys a constitutive law of the form $I_E=a\left(T_1-T_2\right)$. a) Write the result in terms of the current of energy. b) Write the formula in terms of the difference of temperatures. c) Two practical problems having to do with heat transfer are thermal insulation and augmentation of transfer. In the former case one wishes to reduce the transfer rate for a given difference of temperatures. In augmentation the rate of transfer is usually prescribed by the problem, and we want to reduce the temperature difference across the heat exchanger. Show that the seemingly contradictory applications are both an exercise in the minimization of the rate of production of entropy.

Manik Pulyani

Numerade Educator

02:42

Problem 42

A heat pump is used to heat water at $60^{\circ} \mathrm{C}$. Heat is taken from the ground at $2^{\circ} \mathrm{C}$. The observed coefficient of performance is 2.2 while the heating power has a magnitude of 1.0 kW . a) How large is the rate of production of entropy? b) How large is the loss of available power? Show that it is equal to the product of the rate of generation of entropy and the temperature of the environment. c) How large is the second law efficiency of the heat pump?

Shahab Ullah

Numerade Educator

09:56

Problem 43

Water is heated by a heat pump driven by the energy from a thermal power plant. How much entropy may be produced by the dissipative engines if this mode of heating is to be competitive with direct heating of water over a burner?

Vipender Yadav

Numerade Educator

04:08

Problem 44

Derive the formulas for the coefficient of performance and the second law efficiency of a dissipative refrigerator operating between a cold space at temperature $T$ and the environment at $T_a$ in terms of the rate of production of entropy.

Eric Mockensturm

Numerade Educator

06:47

Problem 45

One kilogram of ice is formed from water at $0^{\circ} \mathrm{C}$ in a freezer. The fluid of the engine operates between $-20^{\circ} \mathrm{C}$ and $30^{\circ} \mathrm{C}$, with the temperature of the environment being held at $20^{\circ} \mathrm{C}$. Assume the engine to work reversibly. a) Draw a diagram showing the hotness levels involved and the flow of entropy. Identify sources of entropy production. b) How much entropy is generated? c) How much energy is used for driving the engine in excess of what would be necessary if the engine could operate directly between $0^{\circ} \mathrm{C}$ and $20^{\circ} \mathrm{C}$ ? d) Verify numerically that the excess work (lost available work) is given by the product of the entropy created and the temperature of the environment. e) Verify formally the Gouy-Stodola rule for lost work.

Eric Mockensturm

Numerade Educator

06:11

Problem 46

A refrigerator is designed to pump heat at a specified rate from the cold enclosure. The heat exchanger at the cold end is given; its properties are fixed. If the fluid operating in the Carnot refrigerator works reversibly, which other factors will determine the performance of the engine?

Khoobchandra Agrawal

Numerade Educator

01:58

Problem 47

Compare two methods of heating $50^{\circ} \mathrm{C}$ water. (1) In the first, water at a temperature of $50^{\circ} \mathrm{C}$ is heated further by a solar collector. (2) The radiation of the sun is used to drive an ideal Carnot heat engine between temperatures of $300^{\circ} \mathrm{C}$ and $15^{\circ} \mathrm{C}$. The energy released by this ideal power plant is used to drive an ideal heat pump which gets its entropy at $15^{\circ} \mathrm{C}$ to heat the $50^{\circ} \mathrm{C}$ water. In both cases, $50 \%$ of solar radiation is utilized. a) How large is the ratio of the efficiencies of the methods? b) Determine the ratio of the rates of production of entropy for the methods. Assume solar radiation not to supply any entropy.

Sri Datta Vikas Buchemmavari

Numerade Educator

04:55

Problem 48

Consider the following model of a real heat pump. Entropy flows from a lake which has a temperature of $4^{\circ} \mathrm{C}$ through a heat exchanger into the cold fluid of the heat pump at $-3^{\circ} \mathrm{C}$. It is pumped up to a temperature of $35^{\circ} \mathrm{C}$ by an ideal Carnot heat pump from which it flows through a second heat exchanger into a room; there the temperature measures $22^{\circ} \mathrm{C}$. The thermal energy current associated with the heating of the room is equal to 3.5 kW .
a) How much power is necessary to drive the heat pump? b) How much entropy is produced every second in the system (heat pump plus heat exchangers)?

Vipender Yadav

Numerade Educator

02:47

Problem 49

A liter of water is to be frozen in a freezer. Consider only the process of freezing. a) How much entropy is emitted by the water during this process? b) What is the minimal amount of energy which you have to supply to the freezer if the entropy is to be rejected to the environment at $22^{\circ} \mathrm{C}$ ?

Averell Hause

Carnegie Mellon University

02:06

Problem 50

The heat pump of a house is driven by the electrical energy from a thermal power plant. Take the thermal efficiency of the power plant to be equal to $32 \%$. On the way from the power station to the house, $20 \%$ of the energy will be lost. a) Draw flow diagrams for carriers, energy, and power with the elements consisting of power plant, transmission, and heat pump. b) What should the minimal value of the coefficient of performance of the heat pump be for the balance of energy to be positive compared to an oil burner with an efficiency of $80 \%$ ?

Manish Kumar

Numerade Educator

12:12

Problem 51

An endoreversible engine as in Section 1.7 is to be designed. It consists of the reversible Carnot engine and two heat exchangers serving the furnace and the cooler.
a) Prove that its power at maximum output can be written as

$$
I_{E, \text { mech }}=\frac{(h A)_f}{1+(h A)_f /(h A)_c} T\left[1-\sqrt{\frac{T_o}{T}}\right]^2
$$

where $f$ and $c$ refer to the furnace and the cooler, respectively.
b) If the power is maximized once more by dimensioning relative sizes of the heat exchangers optimally, we get

$$
I_{E, \text { mech }}=\frac{1}{4} h A \cdot T\left[1-\sqrt{\frac{T_o}{T}}\right]^2
$$

where $h A=(h A)_f+(h A)_c$ is the total transfer coefficient multiplying the difference of temperatures.
c) Show that the optimized power of such an engine increases proportionally to ( $\left.T-T_o\right) 2 / T$ for differences of temperatures which are not too large. This condition is quite applicable to today's range of temperatures. What does this mean for the designer of a power plant?

Eric Mockensturm

Numerade Educator

Problem 52

Show that if the heat transfer coefficients of the heat exchangers of an endoreversible power plant are not equal, one should distribute the quantity $h A$ (transfer coefficient times surface area) rather than $A$ equally among the exchangers for the furnace and the cooler.

Check back soon!

04:00

Problem 53

The furnace of a large thermal power plant was designed to deliver energy at a rate of up to 2.0 GW at a temperature of 920 K . Cooling is done at an environmental temperature of 300 K . Model the engine as endoreversible. a) How large is the current of entropy entering the system? b) What is the optimal mechanical power if heat leakage is responsible for a loss of $5 \%$ of the heating power? c) What are the magnitudes of the rate of production of entropy and of the loss of available power? Are they related by the Gouy-Stodola rule?

Rubeena Zulfiqar

Numerade Educator

12:12

Problem 54

Prove that the condition of minimum rate of production of entropy of an endoreversible engine coincides with the condition of maximum power. a) Conduct the proof by directly computing the power of the engine and determining its maximum. b) Can you give a simple argument involving entropy generated and the loss of power to prove the point?

Eric Mockensturm

Numerade Educator

01:47

Problem 55

Derive a general expression for the second law efficiency of an endoreversible engine. Show that it is given by

$$
\eta_2=\frac{1}{1+\sqrt{T_o / T}}
$$

Mahnoor Amin

Numerade Educator

00:46

Problem 56

According to the model of the endoreversible engine with heat exchangers, an ideal Carnot engine running directly between the temperatures of the furnace and the cooler would have zero power. Is there a contradiction between the conclusions drawn from this model and our earlier treatment of the ideal Carnot engine which assumed finite power, as in Equation (10)? [Hint: Remember the discussion concerning ideal walls and where to place the location of the production of entropy.]

Zachary Warner

Numerade Educator

00:57

Problem 57

Model a refrigerator as an endoreversible engine. Its purpose is to pump heat at a prescribed rate out of the cold enclosure. The heat exchangers at the colder and at the warmer end have been dimensioned so as to make the temperature differences across them roughly equal. You now can add a piece of heat exchanger to only one of the existing exchangers. Which one do you choose? Assume the temperature differences across the heat exchangers to be small compared to the temperatures themselves and to the difference of the temperatures of the cold enclosure and the environment. The added piece of heat exchanger is small compared to the existing ones.

Varsha Aggarwal

Numerade Educator

04:53

Problem 58

Consider a solar furnace with heat engine and heat pump as in Example 18. Water is to be heated at constant temperature $T_w$.The engines are supposed to be ideal Carnot engines. Heat (entropy) is supplied to and rejected from engines and reservoirs at constant temperatures. Assume the furnace to be an ideal absorber of solar radiation. The losses from the furnace to the environment are taken to be proportional to the difference of temperatures, Equation (50), with constant heat transfer coefficient $h$. a) Derive the expression for the rate of production of entropy for the entire system. b) How large should the temperature of the furnace be to minimize the production rate of entropy? c) For which value of the temperature of the furnace will the power of the heat engine be a maximum? Why is this value different from the one computed in (b)? Should you try to minimize entropy production or to maximize power output of the heat engine? d) Show that the maximum of the total heating power with which the body of water is being heated occurs at the same temperature of the furnace as that calculated for minimal entropy production.

Eric Mockensturm

Numerade Educator

04:53

Problem 59

Consider the problem of maximizing the available power of the solar thermal system of Example 35. Show that the expression for the total available power attains its maximum if the least amount of entropy is generated.

Eric Mockensturm

Numerade Educator

01:38

Problem 60

A low temperature heat engine employing a traditional coolant such as R 134 is designed for use with normal solar collectors. Estimate the efficiency you might expect from such an engine if heat is collected at $90^{\circ} \mathrm{C}$ and rejected at $30^{\circ} \mathrm{C}$. (A detailed calculation carried out for a particular design gives a value of $9 \%$ to $10 \%$ for the thermal efficiency. T. Koch, Diploma thesis 1993, Technikum Winterthur.)

Varsha Aggarwal

Numerade Educator

02:53

Problem 61

Compare the following traditional statements of the second law with the one given in Section 1.6. Remember that "heat" in these statements is the energy exchanged in heating (or cooling). a) By itself, heat can flow only from hotter to cooler bodies; b) To transfer heat from a place of low temperature to a place of higher temperature, external work must be performed; c) There are no cyclically working engines which continuously withdraw heat from a single heat reservoir, and then transform it into work.

Ashok Prajapati

Numerade Educator

00:21

Problem 62

Compare the statements "By itself heat only flows from hotter to colder places" and "By itself water only flows downhill." Why would one statement be considered something truly noteworthy (the second law of thermodynamics) while the other is taken to be almost trivial? In your opinion do the statements suggest a comparison between heat and water, or between heat and energy?

Zachary Warner

Numerade Educator

00:48

Problem 63

One part of an isolated isothermal body does not spontaneously get hotter at the expense of another part. In two connected water tanks filled to the same level, water does not fill one container spontaneously at the expense of the other. The first phenomenon often is attributed to irreversibility (production of entropy). The second case is explained by noting that you would need energy to pump water from one container into the other (lowering water in the first tank does not provide for enough energy for pumping). Do you agree with the interpretations? Shouldn't the explanations be analogous? If entropy could not be produced would this make possible the heating of a part of an isolated isothermal body at the expense of another?

Sanjeev Kumar

Numerade Educator

01:20

Problem 64

Take a fluid in a container which is perfectly insulated to the flow of heat. We still can perform some operations on the fluid such as compression and expansion, letting an electrical current flow through a wire inside the container, or stirring with the help of a paddle wheel. What kind of experience do we have with the behavior of such a system? Is it true that in general it is impossible to reverse a change once it has occurred? Are there examples of reversible behavior? Does our experience call for a physical quantity which can only increase or stay the same, but never decrease?

Vipender Yadav

Numerade Educator

01:00

Problem 65

Look at the system described in the previous problem (Problem 64). Assume that entropy has the properties we have ascribed to it. Do the types of behavior of the system as we know them from experience follow from these properties?

Averell Hause

Carnegie Mellon University