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Missouri State University

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Problem 106

The $\Delta G$ for the freezing of $\mathrm{H}_{2} \mathrm{O}(l)$ at $-10^{\circ} \mathrm{C}$ is $-210 \mathrm{J} / \mathrm{mol},$ and the heat of fusion of ice at this temperature is 5610 $\mathrm{J} / \mathrm{mol}$ . Find the entropy change of the universe when 1 $\mathrm{mol}$ of water freezes at $-10^{\circ} \mathrm{C} .$

Answer

0.83 $\mathrm{J} / / \mathrm{K}$ .mol

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## Discussion

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## Recommended Questions

The G for the freezing of H2O(l) at -10 C is -210 J>mol, and the heat of fusion of ice at this temperature is 5610 J>mol. Find the entropy change of the universe when 1 mol of water freezes at -10 C.

What is the entropy change to the surroundings when a small decorative ice sculpture at a temperature of $0^{\circ} \mathrm{C}$ and weighing 456 g melts on a granite tabletop, if the temperature of the granite is $12^{\circ} \mathrm{C}$ and the process occurs reversibly? Assume a final temperature for the water of $0^{\circ} \mathrm{C}$. The heat of fusion of ice is $6.01 \mathrm{kJ} / \mathrm{mol} .$

Determine the change in entropy that occurs when 4.3 $\mathrm{kg}$ of water freezes at $0^{\circ} \mathrm{C}$

Calculate the entropy change associated with melting $1.0 \mathrm{kg}$ of ice at $0^{\circ} \mathrm{C}$.

A 65-g ice cube is initially at 0.0°C. (a) Find the change in entropy of the cube after it melts completely at 0.0°C. (b) What is the change in entropy of the environment in this process? Hint: The latent heat of fusion for water is $3.33 \times 10^{5} {J} / {kg}$

Entropy

An 8.0 g ice cube at $-10^{\circ} \mathrm{C}$ is put into a Thermos flask containing 100 $\mathrm{cm}^{3}$ of water at $20^{\circ} \mathrm{C}$ . By how much has the entropy of the cube-water system changed when equilibrium is reached? The specific heat of ice is 2220 $\mathrm{J} / \mathrm{kg} \cdot \mathrm{K}$.

(I) What is the change in entropy of 1.00 $\mathrm{m}^{3}$ of water at $0^{\circ} \mathrm{C}$

when it is frozen to ice at $0^{\circ} \mathrm{C} ?$

Entropy

A mixture of 1773 g of water and 227 g of ice is in an initial equilibrium state at $0.000^{\circ} \mathrm{C}$ . The mixture is then, in a reversible process, brought to a second equilibrium state where the water-ice ratio, by mass, is $1.00 : 1.00$ at $0.000^{\circ} \mathrm{C}$ (a) Calculate the entropy change of the system during this process. (The heat of fusion for water is 333 $\mathrm{kJ} / \mathrm{kg} .$ ) (b) The system is then returned to the initial equilibrium state in an irreversible process (say, by using a Bunsen burner). Calculate the entropy change of the system during this process. (c) Are your answers consistent with the second law of thermodynamics?

Calculate the change in entropy that occurs in the system when 55.0 g of water vaporizes from a liquid to a gas at its boiling point $\left(100.0^{\circ} \mathrm{C}\right) .$ See Table 11.7 for heats of vaporization.

(a) What is the entropy change of 1.00 mol of $\mathrm{H}_{2} \mathrm{O}$ when it changes from ice to water at $0.0^{\circ} \mathrm{C} ?$ (b) If the ice is in contact with an environment at a temperature of $10.0^{\circ} \mathrm{C}$ what is the entropy change of the universe when the ice melts?

Entropy

(a) What is the entropy change of a 12.0 g ice cube that melts completely in a bucket of water whose temperature is just above the freezing point of water? (b) What is the entropy change of a 5.00 g spoonful of water that evaporates completely on a hot plate whose temperature is slightly above the boiling point of water?

A freezer is used to freeze 1.0 $\mathrm{L}$ of water completely into ice. The water and the freezer remain at a constant temperature of $T=0^{\circ} \mathrm{C}$ . Determine (a) the change in the entropy of the water and (b) the change in the entropy of the freezer.

Calculate the change in entropy that occurs in the system when 55.0 g of water vaporizes from a liquid to a gas at its boiling point (100.0 C). See Table 11.7 for heats of vaporization.

Making lce You place 0.410 $\mathrm{kg}$ of cold water inside a freezer that has a constant temperature of $0^{\circ} \mathrm{C}$ . The water eventually freezes

and becomes ice at $0^{\circ} \mathrm{C}$ (a) What is the change in entropy of the

water as it turns into ice? (See Table $17-4$ for the appropriate latent

heat.) (b) If the coefficient of performance of the freezer is $4.50,$ how much heat does the freezer exhaust into your kitchen as a result

of freezing the water? (c) If your kitchen temperature is $22^{\circ} \mathrm{C}$ , what

is the increase in entropy of your kitchen? (d) What is the change

in entropy of the universe during the freezing process?

(II) If 1.00 $\mathrm{m}^{3}$ of water at $0^{\circ} \mathrm{C}$ is frozen and cooled to $-10^{\circ} \mathrm{C}$

by being in contact with a great deal of ice at $-10^{\circ} \mathrm{C}$

estimate the total change in entropy of the process.

Entropy

A 10 $\mathrm{g}$ ice cube at $-10^{\circ} \mathrm{C}$ is placed in a lake whose temperature is $15^{\circ} \mathrm{C}$ . Calculate the change in entropy of the cube-lake system as the ice cube comes to thermal equilibrium with the lake. The specific heat of ice is 2220 $\mathrm{J} / \mathrm{kg} \cdot \mathrm{K}$ . (Hint: Will the ice cube affect the lake temperature?

An ice cube with a mass of 20 $\mathrm{g}$ at $-20^{\circ} \mathrm{C}$ (typical freezer temperature) is dropped into a cup that holds 500 $\mathrm{mL}$ of hot water, initially at $83^{\circ} \mathrm{C} .$ What is the final temperature in the cup? The density of liquid water is 1.00 $\mathrm{g} / \mathrm{mL}$ ; the specific heat capacity of ice is $2.03 \mathrm{J} / \mathrm{g}-\mathrm{C}$ ; the specific heat capacity of liquid water is $4.184 \mathrm{J} / \mathrm{g}-\mathrm{C} ;$ the enthalpy of

fusion of water is 6.01 $\mathrm{k} \mathrm{J} / \mathrm{mol} .$

Find the change in entropy when 1.85 kg of water at $100^{\circ} \mathrm{C}$ is boiled away to steam at $100^{\circ} \mathrm{C}$

(I) What is the change in entropy of 1.00 m$^3$ of water at 0$^\circ$C when it is frozen to ice at 0$^\circ$C?

(a) Ten grams of $\mathrm{H}_{2} \mathrm{O}$ starts as ice at $0^{\circ} \mathrm{C}$. The ice absorbs heat from the air (just above $0^{\circ} \mathrm{C}$ ) until all of it melts. Calculate the entropy change of the $\mathrm{H}_{2} \mathrm{O}$, of the air, and of the universe. (b) Suppose that the air in part (a) is at $20^{\circ} \mathrm{C}$ rather than $0^{\circ} \mathrm{C}$ and that the ice absorbs heat until it becomes water at $20^{\circ} \mathrm{C}$. Calculate the entropy change of the $\mathrm{H}_{2} \mathrm{O}$, of the air, and of the universe. (c) Is either of these processes reversible?

Entropy

Energy can be removed from water as heat at and even below the normal freezing point ($0.0^{\circ} \mathrm{C}$ at atmospheric pressure) without causing the water to freeze; the water is then said to be supercooled. Suppose a 1.00 g water drop is super-cooled until its temperature is that of the surrounding air, which is at $-5.00^{\circ} \mathrm{C} .$ The drop then suddenly and irreversibly freezes, transferring energy to the air as heat. What is the entropy change for the drop? (Hint: Use a three-step reversible process as if the water were taken through the normal freezing point.) The specific heat of ice is 2220 $\mathrm{J} / \mathrm{kg} \cdot \mathrm{K}$.

Calculate the change in entropy that occurs in the system when 45.0 g of acetone (C3H6O) freezes at its melting point (-94.8 C). See Table 11.9 for heats of fusion.

(a) After 6.00 $\mathrm{kg}$ of water at $85.0^{\circ} \mathrm{C}$ is mixed in a perfect thermos with 3.00 $\mathrm{kg}$ of ice at $0.0^{\circ} \mathrm{C},$ the mixture is allowed to reach equilibrium. When heat is added to or removed from a solid or liquid of mass $m$ and specific heat capacity $c$ , the change in entropy can be shown to be $\Delta S=m c \ln \left(T_{\mathrm{f}} / T_{\mathrm{i}}\right),$ where $T_{\mathrm{i}}$ and $T_{\mathrm{f}}$ are the initial and final Kelvin temperatures. Using this expression and the change in entropy for melting, find the change in entropy that occurs. $(\mathrm{b})$ Should the entropy of the universe increase or decrease as a result of the mixing process? Give your reasoning and state whether your answer in part (a) is consistent with your answer here.

Another decorative "ice" sculpture is carved from dry ice (solid $\mathrm{CO}_{2}$ ) and held at its sublimation point of $-78.5^{\circ} \mathrm{C} .$ What is the entropy change to the universe when the $\mathrm{CO}_{2}$ sculpture, weighing $389 \mathrm{g},$ sublimes on a granite tabletop if the temperature of the granite is $12^{\circ} \mathrm{C}$ and the process occurs reversibly? Assume a final temperature for the $\mathrm{CO}_{2}$ vapor of $-78.5^{\circ} \mathrm{C} .$ The heat of sublimation of $\mathrm{CO}_{2}$ is $26.1 \mathrm{kJ} / \mathrm{mol}$.

Estimate the entropy change of $850 \mathrm{g}$ of water when it is heated from $20.0^{\circ} \mathrm{C}$ to $50.0^{\circ} \mathrm{C} .$ [Hint: Assume that the heat flows into the water at an average temperature. $]$

Calculate the change in entropy that occurs in the system when 1.00 mole of isopropyl alcohol $\left(\mathrm{C}_{3} \mathrm{H}_{8} \mathrm{O}\right)$ melts at its melting point $\left(-89.5^{\circ} \mathrm{C}\right) .$ See Table 11.9 for heats of fusion.

Use standard enthalpies of formation to calculate the standard change in enthalpy for the melting of ice. (The $\Delta H_{1}^{\circ}$ for $\mathrm{H}_{2} \mathrm{O}(s)$ is $-291.8 \mathrm{kJ} / \mathrm{mol} .$ ) Use this value to calculate the mass of ice required to cool 355 $\mathrm{mL}$ of a beverage from room temperature $\left(25.0^{\circ} \mathrm{C}\right)$ to $0.0^{\circ} \mathrm{C}$ Assume that the specific heat capacity and density of the beverage are the same as those of water.

A 20.0 -g sample of ice at $-10.0^{\circ} \mathrm{C}$ is mixed with 100.0 g water at $80.0^{\circ} \mathrm{C}$ . Calculate the final temperature of the mixture assuming no heat loss to the surroundings. The heat capacities of $\mathrm{H}_{2} \mathrm{O}(s)$ and $\mathrm{H}_{2} \mathrm{O}(l)$ are 2.03 and $4.18 \mathrm{J} / \mathrm{g} \cdot^{\circ} \mathrm{C},$ respectively, and the enthalpy of fusion for ice is 6.02 $\mathrm{kJ} / \mathrm{mol} .$

Two hundred grams of water at $0^{\circ} \mathrm{C}$ is brought into contact with a heat reservoir at $80^{\circ} \mathrm{C}$. After themal equilibrium is reached, what is the temperature of the water? Of the reservoir? How much heat has been transferred in the process? What is the entropy change of the water? Of the reservoir? What is the entropy change of the universe?

Entropy

An insulated Thermos contains 130 g of water at $80.0^{\circ} \mathrm{C}$ You put in a 12.0 g ice cube at $0^{\circ} \mathrm{C}$ to form a system of $i c e+$ original water. (a) What is the equilibrium temperature of the system? What are the entropy changes of the water that was originally the ice cube (b) as it melts and (c) as it warms to the equilibrium temperature? (d) What is the entropy change of the original water as it cools to the equilibrium temperature? (e) What is the net entropy change of the $i c e+$ original water system as it reaches the equilibrium temperature?

You heat $250 \mathrm{g}$ of water from $10^{\circ} \mathrm{C}$ to $95^{\circ} \mathrm{C} .$ By how much does the entropy of the water increase?

Suppose $20 \mathrm{g}$ of ice at $0^{\circ} \mathrm{C}$ is added to $300 \mathrm{g}$ of water at $60^{\circ} \mathrm{C}$. What is the total change in entropy of the mixture after it reaches thermal equilibrium?

An 8.5 g ice cube is placed into 255 g of water. Calculate the temperature change in the water upon the complete melting of the ice. Assume that all of the energy required to melt the ice comes from the water.

An 8.5-g ice cube is placed into 255 g of water. Calculate the temperature change in the water upon the complete melting of the ice. Assume that all of the energy required to melt the ice comes from the water.

An ice cube at $0.0^{\circ} \mathrm{C}$ is slowly melting. What is the change in the ice cube's entropy for each $1.00 \mathrm{g}$ of ice that melts?

Find the change in entropy of the $\mathrm{H}_{2} \mathrm{O}$ molecules when (a) three kilograms of ice melts into water at 273 $\mathrm{K}$ and $(\mathrm{b})$ three kilograms of water changes into steam at 373 $\mathrm{K}$ . (c) On the basis of the answers to parts (a) and (b), discuss which change creates more disorder in the collection of $\mathrm{H}_{2} \mathrm{O}$ molecules.

Two hundred grams of water at $0^{\circ} \mathrm{C}$ is brought into contact into thermal equilibrium successively with contact reservoirs at $20^{\circ} \mathrm{C}, 40^{\circ} \mathrm{C}, 60^{\circ} \mathrm{C},$ and $80^{\circ} \mathrm{C} .$ (a) What is the entropy change of the water? (b) Of the reservoir? (c) What is the entropy change of the universe?

A reaction has $\Delta H_{\mathrm{rxn}}^{\circ}=-112 \mathrm{kJ}$ and $\Delta S_{\mathrm{rxn}}^{\circ}=354 \mathrm{J} / \mathrm{K}$ . At what temperature is the change in entropy for the reaction equal to the change in entropy for the surroundings?

A freezer is used to freeze 1.0 L of water completely into ice. The water and the freezer remain at a constant temperature of T 5 0°C. Determine (a) the change in the entropy of the water and (b) the change in the entropy of the freezer.

Find $\Delta E, \Delta H, q,$ and $w$ for the change in state of 1.0 $\mathrm{mol} \mathrm{H}_{2} \mathrm{O}(l)$ at $80^{\circ} \mathrm{C}$ to $\mathrm{H}_{2} \mathrm{O}(g)$ at $110^{\circ} \mathrm{C} .$ The heat capacity of $\mathrm{H}_{2} \mathrm{O}(l)$ at $=75.3 \mathrm{J} / \mathrm{mol} \mathrm{K},$ heat capacity of $\mathrm{H}_{2} \mathrm{O}(g)=25.0 \mathrm{J} / \mathrm{mol} \mathrm{K},$ and the heat of vaporization of $\mathrm{H}_{2} \mathrm{O}$ is $40.7 \times 10^{3} \mathrm{J} / \mathrm{mol}$ at $100^{\circ} \mathrm{C}$ .

What is the decrease in entropy of 25.0 g of water that condenses on a bathroom mirror at a temperature of $35.0^{\circ} \mathrm{C},$ assuming no change in temperature and given the latent heat of vaporization to be 2450 $\mathrm{kJ} / \mathrm{kg}$ ?

(a) Calculate the change in entropy when 1.00 kg of water at 100$^\circ$C is vaporized and converted to steam at 100$^\circ$C (see Table 17.4). (b) Compare your answer to the change in entropy when 1.00 kg of ice is melted at 0$^\circ$C, calculated in Example 20.5 (Section 20.7). Is the change in entropy greater for melting or for vaporization? Interpret your answer using the idea that entropy is a measure of the randomness of a system.

(II) Calculate the change in entropy of 1.00 $\mathrm{kg}$ of water when it is heated from $0^{\circ} \mathrm{C}$ to $75^{\circ} \mathrm{C}$ (a) Make an estimate; (b) use the integral $\Delta S=\int d Q / T .$ (c) Does the entropy of the surroundings change? If so, by how much?

The heat of vaporization of water at 373 $\mathrm{K}$ is 40.7 $\mathrm{kJ} / \mathrm{mol} .$ Find $q$

$w, \Delta E,$ and $\Delta H$ for the evaporation of 454 $\mathrm{g}$ of water at this temperature at 1 $\mathrm{atm} .$

Calculate the change in entropy that occurs in the system when 1.00 mole of isopropyl alcohol (C3H8O) melts at its melting point (-89.5 C). See Table 11.9 for heats of fusion.

The dissolution of $\mathrm{NH}_{4} \mathrm{ClO}_{4}(s)$ in water is endothermic, with $\Delta H_{\text { soln }}=+33.5 \mathrm{kJ} / \mathrm{mol} .$ If you prepare a 1.00 $\mathrm{m}$ solu-

tion of $\mathrm{NH}_{4} \mathrm{ClO}_{4}$ beginning with water at $25.0^{\circ} \mathrm{C},$ what is

the final temperature of the solution in $^{\circ} \mathrm{C} ?$ Assume that the

specific heats of both pure $\mathrm{H}_{2} \mathrm{O}$ and the solution are the

same, 4.18 $\mathrm{J} /(\mathrm{K} \cdot \mathrm{g})$

An ice cube tray contains enough water at $22.0^{\circ} \mathrm{C}$ to make 18 ice cubes that each has a mass of 30.0 $\mathrm{g} .$ The tray is placed in a freezer that uses $\mathrm{CF}_{2} \mathrm{Cl}_{2}$ as a refrigerant. The heat of vaporization of $\mathrm{CF}_{2} \mathrm{Cl}_{2}$ is 158 $\mathrm{J} / \mathrm{g}$ . What mass of $\mathrm{CF}_{2} \mathrm{Cl}_{2}$ must be vaporized in the refrigeration cycle to convert all the water at $22.0^{\circ} \mathrm{C}$ to ice at $-5.0^{\circ} \mathrm{C} ?$ The heat capacities for $\mathrm{H}_{2} \mathrm{O}(s)$ and $\mathrm{H}_{2} \mathrm{O}(l)$ are 2.03 $\mathrm{J} / \mathrm{g} \cdot^{\circ} \mathrm{C}$ and 4.18 $\mathrm{J} / \mathrm{g} \cdot^{\circ} \mathrm{C}$ , respectively, and the enthalpy of fusion for ice is 6.02 $\mathrm{kJ} / \mathrm{mol} .$

An ice cube tray contains enough water at $22.0^{\circ} \mathrm{C}$ to make 18 ice cubes that each has a mass of $30.0 \mathrm{g}$. The tray is placed in a freezer that uses $\mathrm{CF}_{2} \mathrm{Cl}_{2}$ as a refrigerant. The heat of vaporization of $\mathrm{CF}_{2} \mathrm{Cl}_{2}$ is $158 \mathrm{J} / \mathrm{g} .$ What mass of $\mathrm{CF}_{2} \mathrm{Cl}_{2}$ must be vaporized in the refrigeration cycle to convert all the water at $22.0^{\circ} \mathrm{C}$ to ice at $-5.0^{\circ} \mathrm{C} ?$ The heat capacities for $\mathrm{H}_{2} \mathrm{O}(s)$ and $\mathrm{H}_{2} \mathrm{O}(l)$ are $2.03 \mathrm{J} / \mathrm{g} \cdot^{\circ} \mathrm{C}$ and $4.18 \mathrm{J} / \mathrm{g} \cdot^{\circ} \mathrm{C},$ respectively, and the

enthalpy of fusion for ice is $6.02 \mathrm{kJ} / \mathrm{mol}$.

A 250 -g sample of water at $80^{\circ} \mathrm{C}$ is mixed with $250 \mathrm{g}$ of water at $10^{\circ} \mathrm{C} .$ Find the entropy changes for (a) the hot water, (b) the cool water, and (c) the system.

A $20.0-\mathrm{g}$ sample of ice at $-10.0^{\circ} \mathrm{C}$ is mixed with $100.0 \mathrm{g}$ water at $80.0^{\circ} \mathrm{C}$. Calculate the final temperature of the mixture assuming no heat loss to the surroundings. The heat capacities of $\mathrm{H}_{2} \mathrm{O}(s)$ and $\mathrm{H}_{2} \mathrm{O}(l)$ are 2.03 and $4.18 \mathrm{J} / \mathrm{g} \cdot^{\circ} \mathrm{C},$ respectively, and the enthalpy of fusion for ice is $6.02 \mathrm{kJ} / \mathrm{mol}$.

A sophomore with nothing better to do adds heat to

0.350 $\mathrm{kg}$ of ice at $0.00^{\circ} \mathrm{C}$ until it is all melted. (a) What is the

change in entropy of the water? (b) The source of the heat is a very massive body at a temperature of $25.0^{\circ} \mathrm{C}$ . What is the

change in entropy of this body? (c) What is the total change in

entropy of the water and the heat source?

Find the entropy change when a 2.4 -kg aluminum pan at $155^{\circ} \mathrm{C}$ is plunged into $3.5 \mathrm{kg}$ of water at $15^{\circ} \mathrm{C}$

(I) What is the change in entropy of 250 $\mathrm{g}$ of steam at $100^{\circ} \mathrm{C}$

when it is condensed to water at $100^{\circ} \mathrm{C} ?$

Entropy

Find (a) the energy absorbed as heat and (b) the change in entropy of a 2.00 $\mathrm{kg}$ block of copper whose temperature is increased reversibly from $25.0^{\circ} \mathrm{C}$ to $100^{\circ} \mathrm{C}$ . The specific heat of copper is 386 $\mathrm{J} / \mathrm{kg} \cdot \mathrm{K}$ .

The element gallium (Ga) freezes at $29.8^{\circ} \mathrm{C},$ and its molar enthalpy of fusion is $\Delta H_{\text { fus }}=5.59 \mathrm{k} \mathrm{k} / \mathrm{mol}$ . (a) When molten gallium solidifies to Ga(s) at its normal melting point, is $\Delta S$ positive or negative? (b) Calculate the value of $\Delta S$ when 60.0 g of Ga(l) solidifies at $29.8^{\circ} \mathrm{C}$ .

The specific heat of solid copper is $0.385 \mathrm{J} / \mathrm{g} \cdot^{\circ} \mathrm{C}$ ). What thermal energy change occurs when a $35.3 \mathrm{g}$ sample of copper is cooled from $35.0^{\circ} \mathrm{C}$ to $15.0^{\circ} \mathrm{C} ?$ Be sure to give your answer the proper sign. This amount of energy is used to melt solid ice at $0.0^{\circ} \mathrm{C} .$ The molar enthalpy of fusion of ice is $6.01 \mathrm{kJ} / \mathrm{mol} .$ How many moles of ice are melted?

The temperature of a 0.700 $\mathrm{kg}$ cube of ice is decreased to $-150^{\circ} \mathrm{C} .$ Then energy is gradually transferred to the cube as heat while it is otherwise thermally isolated from its environment. The total transfer is 0.6993 $\mathrm{MJ}$ . Assume the value of $c_{\text { ice given in Table } 18-3}$ is valid for temperatures from $-150^{\circ} \mathrm{C}$ to $0^{\circ} \mathrm{C} .$ What is the final temperature of the water?

What is the change in entropy when 0.200 mol of potassium freezes at $63.7^{\circ} \mathrm{C}\left(\Delta H_{\text { fus }}=2.39 \mathrm{kJ} / \mathrm{mol}\right) ?$

A shallow pond contains 94 Mg of water. In winter, it's entirely frozen. By how much does the entropy of the pond increase when the ice, already at $0^{\circ} \mathrm{C}$, melts and then heats to its summer temperature of $15^{\circ} \mathrm{C} ?$

Given that the heat of fusion of water is -6.02 kJ>mol, the heat capacity of H2O(l) is 75.2 J>mol # K, and the heat capacity of H2O(s) is 37.7 J>mol # K, calculate the heat of fusion of water at -10 C.

Additional Problems

A 0.600 kg sample of water is initially ice at temperature $-20^{\circ} \mathrm{C} .$ What is the sample's entropy change if its temperature is increased to $40^{\circ} \mathrm{C} ?$

Use standard enthalpies of formation to calculate the standard change in enthalpy for the melting of ice. (The Hf for H2O(s) is -291.8 kJ>mol.) Use this value to calculate the mass of ice required to cool 355 mL of a beverage from room temperature (25.0 C) to 0.0 C. Assume that the specific heat capacity and

density of the beverage are the same as those of water.

Challenge If 335 g of water at $65.5^{\circ} \mathrm{C}$ loses 9750 $\mathrm{J}$ of heat, what is the final temperature

of the water?

A Styrofoam cup holding 125 $\mathrm{g}$ of hot water at $1.00 \times 10^{2 \circ} \mathrm{C}$ cools to room temperature, $20.0^{\circ} \mathrm{C}$ . What is the change in entropy of the room? (Neglect the specific heat of the cup and any change in temperature of the room.)

Relating ldeas Given the entropy change for the first

two reactions below, calculate the entropy change for

the third reaction below.

$\mathrm{S}_{8}(s)+8 \mathrm{O}_{2}(s) \longrightarrow 8 \mathrm{SO}_{2}(g) \qquad \Delta S=89 \mathrm{J} / \mathrm{K}$

$2 \mathrm{SO}_{2}(s)+\mathrm{O}_{2}(s) \longrightarrow 2 \mathrm{SO}_{3}(g) \qquad \Delta S=-188 \mathrm{J} / \mathrm{K}$

$\mathrm{S}_{8}(s)+12 \mathrm{O}_{2}(s) \longrightarrow 8 \mathrm{SO}_{3}(g) \qquad \Delta S=?$

What is the entropy of fusion, $\Delta S_{\text { fusion in }} \mathrm{J} /(\mathrm{K} \cdot \text { mol) for }$ sodium? The necessary data are given in Problem 10.61

Fifty grams of water at $0^{\circ} \mathrm{C}$ are changed into vapor at $100^{\circ} \mathrm{C}$. What is the change in entropy of the water in this process?

A sophomore with nothing better to do adds heat to 0.350 kg of ice at 0.0$^\circ$C until it is all melted. (a) What is the change in entropy of the water? (b) The source of heat is a very massive body at 25.0$^\circ$C. What is the change in entropy of this body? (c) What is the total change in entropy of the water and the heat source?

A 126.5 -g insulated aluminum cup at $18.00^{\circ} \mathrm{C}$ is filled with

132.5 $\mathrm{g}$ of water at $46.25^{\circ} \mathrm{C}$ . After a few minutes, equilibrium

is reached. Determine $(a)$ the final temperature, and $(b)$ the

total change in entropy.

A $40 .$ -g block of ice is cooled to $-78^{\circ} \mathrm{C}$ and is then added to 560 $\mathrm{g}$ of water in an 80 -g copper calorimeter at a temperature of $25^{\circ} \mathrm{C}$ . Determine the final temperature of the system consisting of the ice, water, and calorimeter. (If not all the ice melts, determine how much ice is left.) Remember that the ice must first warm to $0^{\circ} \mathrm{C}$ , melt, and then continue warming as water. (The specific heat of ice is $0.500 \mathrm{cal} / \mathrm{g} \cdot^{\circ} \mathrm{C}=2090 \mathrm{J} / \mathrm{kg} \cdot^{\circ} \mathrm{C} .$ .

A 70.0 -kg log falls from a height of 25.0 $\mathrm{m}$ into a lake. If the log, the lake, and the air are all at $300 . \mathrm{K}$ , find the change in entropy of the Universe during this process.

Fifty grams of water at $20^{\circ} \mathrm{C}$ is heated until it becomes vapor at $100^{\circ} \mathrm{C}$. Calculate the change in entropy of the water in this process.

What is the entropy change of $10 \mathrm{g}$ of steam at $100^{\circ} \mathrm{C} \quad$ when it condenses to water at the same temperature?

(I) What is the change in entropy of 320 g of steam at 100$^\circ$C when it is condensed to water at 100$^\circ$C?

The freezing point of mercury is $-38.8^{\circ} \mathrm{C} .$ What quantity of heat energy, in joules, is released to the surroundings if $1.00 \mathrm{mL}$ of mercury is cooled from $23.0^{\circ} \mathrm{C}$ to $-38.8^{\circ} \mathrm{C}$ and then frozen to a solid? (The density of liquid mercury is $13.6 \mathrm{g} / \mathrm{cm}^{3} .$ Its specific heat capacity is $0.140 \mathrm{J} / \mathrm{g} \cdot \mathrm{K}$ and its heat of fusion is $11.4 \mathrm{J} / \mathrm{g} .$ )

Estimate the total change in entropy of two containers of water. One container holds 0.1 $\mathrm{kg}$ of water at $70^{\circ} \mathrm{C}$ and is warmed to $90^{\circ} \mathrm{C}$ by heating from contact with the other container. The other container, also holding 0.1 $\mathrm{kg}$ of water, cools from $30^{\circ} \mathrm{C}$ to $10^{\circ} \mathrm{C}$ . Is this energy transfer process allowed by the first law of thermodynamics? By the second?

(a) Determine the final temperature when 0.1 $\mathrm{kg}$ of wa-ter at $10^{\circ} \mathrm{C}$ is added to 0.3 $\mathrm{kg}$ of soup at $50^{\circ} \mathrm{C} .$ What assumptions did you make? (b) Estimate the entropy change of this water-soup system during the process. Does the second law of

thermodynamics allow this process?

What is the entropy change when the volume of 1.6 $\mathrm{g}$ of $\mathrm{O}_{2}$ increases from 2.5 $\mathrm{L}$ to 3.5 $\mathrm{L}$ at a constant temperature of $75^{\circ} \mathrm{C} ?$ Assume that $\mathrm{O}_{2}$ behaves as an ideal gas.

(I) 1.0 kg of water is heated from 0$^\circ$C to 100$^\circ$C. Estimate the change in entropy of the water.

Find the change in entropy as $2.00 \mathrm{kg}$ of $\mathrm{H}_{2} \mathrm{O}$ at $100^{\circ} \mathrm{C}$ turns to vapor at the same temperature.

Tell whether the entropy changes, $\Delta S,$ for the following processes are likely to be positive or negative:

(a) The conversion of liquid water to water vapor at $100^{\circ} \mathrm{C}$

(b) The freezing of liquid water to ice at $0^{\circ} \mathrm{C}$

(c) The eroding of a mountain by a glacier

You make tea with 0.250 kg of 85.0$^\circ$C water and let it cool to room temperature (20.0$^\circ$C). (a) Calculate the entropy change of the water while it cools. (b) The cooling process is essentially isothermal for the air in your kitchen. Calculate the change in entropy of the air while the tea cools, assuming that all of the heat lost by the water goes into the air. What is the total entropy change of the system tea + air?

What quantity of heat is evolved when 1.0 L of water at $0^{\circ} \mathrm{C}$ solidifies to ice? The heat of fusion of water is $333 \mathrm{J} / \mathrm{g} .$

A $500-\mathrm{g}$ copper block at $80^{\circ} \mathrm{C}$ is dropped into $1.0 \mathrm{kg}$ of water at $10^{\circ} \mathrm{C}$. Find (a) the final temperature and (b) the entropy change of the system.

. An ice-cube tray contains 0.350 $\mathrm{kg}$ of water at $18.0^{\circ} \mathrm{C}$ . How much heat must be removed from the water to cool it to $0.00^{\circ} \mathrm{C}$ and freeze it? Express your answer in joules and in calories.

Find the increase in entropy of 1.00 $\mathrm{kg}$ of liquid nitrogen that starts at its boiling temperature, boils, and warms to $20.0^{\circ} \mathrm{C}$ at constant pressure.