Thermal Physics : Kinetic Theory, Thermodynamics and Statistical Mechanics

S.C. Garg, R.M. Bansal, C.K. Ghosh

Chapter 6

The Second Law of Thermodynamics - all with Video Answers

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Chapter Questions

Problem 1

An ideal gas engine operates in a cycle, which when represented on a $p-V$ diagram, is a rectangle. If we call $p_{1}, p_{2}$ the lower and higher pressures respectively and $V_{1}$, $V_{2}$ corresponding volumes,
(a) Calculate the work done in one complete cycle.
(b) Indicate in which parts of the cycle heat is absorbed and in which part librated. Calculate the quantity of heat flowing into the gas in one cycle, and
(c) Show that the efficiency of the engine is

Surendra Kumar

Surendra Kumar

Numerade Educator

Problem 2

Figure $6.19$ shows the $p-V$ diagram of an ideal engine. All processes are quasistatic and $C_{p}$ is a constant. Prove that the efficiency of the engine is given by
$$
\eta=1-\left(\frac{p_{a}}{p_{b}}\right)^{\frac{\gamma-1}{\gamma}}
$$

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Numerade Educator

Problem 3

Hydrogen is used in a Carnot cycle as a working substance. Calculate the efficiency of the cycle if in an adiabatic expansion
(a) the volume of the gas is doubled, and
(b) the pressure of the gas is halved

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Problem 4

An ideal gas goes through a cycle consisting of
(a) isochoric, adiabatic and isothermal lines,
(b) isobaric, adiabatic and isothermal lines When the isothermal occurs at the minimum temperature, calculate the efficiency of each cycle if the absolute temperature varies $n-1$ fold within the cycle.

Surendra Kumar

Numerade Educator

Problem 5

Calculate the minimum amount of work in joules required to freeze one gram of water at $0^{\circ} \mathrm{C}$ by means of an engine which operates in surroundings at $25^{\circ} \mathrm{C}$. Given latent heat of ice is $80 \mathrm{cal} \mathrm{g}^{-1}$.

Ashok Prajapati

Ashok Prajapati

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Problem 6

The cold reservoir of a Carnot engine is at $7^{\circ} \mathrm{C}$. Its efficiency is $40 \%$ which is to be increased to $50 \%$.
(a) By how many degrees the temperature of the hot reservoir must be increased if the temperature of the cold reservoir is kept constant?
(b) By how many degrees the temperature of the cold reservoir be decreased if the temperature of hot reservoir is kept constant?

Ajay Singhal

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Problem 7

A thermal power plant generating $1000 \mathrm{MW}$ of electrical power is located by the side of a river. The overall efficiency of the plant is $40 \%$.
(a) What is the total thermal power input to the plant?
(b) At what rate is waste heat discharged from the plant?
(c) If the waste heat is delivered to the river, and if a temperature rise of no more than $5^{\circ} \mathrm{C}$ is permissible, how much water must be available per second?

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Problem 8

When the sun shines on a glass-roofed greenhouse, the temperature inside becomes higher than outside. Does this violate the second law of thermodynamics?

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Problem 9

A reversible engine converts one-third of heat into work. When the temperature of the sink is reduced by $100^{\circ} \mathrm{C}$, it converts one-half of heat input into work. Calculate the temperatures of the source and the sink.

Ajay Singhal

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Problem 10

A refrigerator is fitted with a motor of $200 \mathrm{~W}$. The temperature of its freezing compartment is $-3^{\circ} \mathrm{C}$ and that of the room air is $27^{\circ} \mathrm{C}$. Calculate the maximum amount of heat which the refrigerator can remove from the freezing compartment in 10 minutes.

Ashok Prajapati

Ashok Prajapati

Numerade Educator

Problem 11

The temperature of a household refrigerator is $5^{\circ} \mathrm{C}$ and the room temperature is $30^{\circ} \mathrm{C}$. Nearly $3 \times 10^{8} \mathrm{~J}$ heat flows from the room to the refrigerator in a day and has to be pumped out of the refrigerator to maintain its temperature. If the coefficient of performance of the refrigerator is $60 \%$ of the efficiency of a Carnot engine working between the same temperature limits, calculate the power required to run the refrigerator.

Surendra Kumar

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Problem 12

In an air standard Otto cycle, $1000 \mathrm{~kJ} \mathrm{~kg}^{-1}$ net work is done. The maximum temperature in the cycle is $3200 \mathrm{~K}$ and the temperature at the end of the compression stroke is $800 \mathrm{~K}$. Calculate the compression ratio of the engine.

Surendra Kumar

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