# 15.6 Entropy and the second law of thermodynamics: disorder and  (Page 7/10)

 Page 7 / 10

## Section summary

• Entropy is the loss of energy available to do work.
• Another form of the second law of thermodynamics states that the total entropy of a system either increases or remains constant; it never decreases.
• Entropy is zero in a reversible process; it increases in an irreversible process.
• The ultimate fate of the universe is likely to be thermodynamic equilibrium, where the universal temperature is constant and no energy is available to do work.
• Entropy is also associated with the tendency toward disorder in a closed system.

## Conceptual questions

A woman shuts her summer cottage up in September and returns in June. No one has entered the cottage in the meantime. Explain what she is likely to find, in terms of the second law of thermodynamics.

Consider a system with a certain energy content, from which we wish to extract as much work as possible. Should the system’s entropy be high or low? Is this orderly or disorderly? Structured or uniform? Explain briefly.

Does a gas become more orderly when it liquefies? Does its entropy change? If so, does the entropy increase or decrease? Explain your answer.

Explain how water’s entropy can decrease when it freezes without violating the second law of thermodynamics. Specifically, explain what happens to the entropy of its surroundings.

Is a uniform-temperature gas more or less orderly than one with several different temperatures? Which is more structured? In which can heat transfer result in work done without heat transfer from another system?

Give an example of a spontaneous process in which a system becomes less ordered and energy becomes less available to do work. What happens to the system’s entropy in this process?

What is the change in entropy in an adiabatic process? Does this imply that adiabatic processes are reversible? Can a process be precisely adiabatic for a macroscopic system?

Does the entropy of a star increase or decrease as it radiates? Does the entropy of the space into which it radiates (which has a temperature of about 3 K) increase or decrease? What does this do to the entropy of the universe?

Explain why a building made of bricks has smaller entropy than the same bricks in a disorganized pile. Do this by considering the number of ways that each could be formed (the number of microstates in each macrostate).

## Problem exercises

(a) On a winter day, a certain house loses $5\text{.}\text{00}×{\text{10}}^{8}\phantom{\rule{0.25em}{0ex}}\text{J}$ of heat to the outside (about 500,000 Btu). What is the total change in entropy due to this heat transfer alone, assuming an average indoor temperature of $\text{21.0º C}$ and an average outdoor temperature of $5.00º C$ ? (b) This large change in entropy implies a large amount of energy has become unavailable to do work. Where do we find more energy when such energy is lost to us?

(a) $9.78×{\text{10}}^{4}\phantom{\rule{0.25em}{0ex}}\text{J/K}$

(b) In order to gain more energy, we must generate it from things within the house, like a heat pump, human bodies, and other appliances. As you know, we use a lot of energy to keep our houses warm in the winter because of the loss of heat to the outside.

On a hot summer day, $4\text{.}\text{00}×{\text{10}}^{6}\phantom{\rule{0.25em}{0ex}}\text{J}$ of heat transfer into a parked car takes place, increasing its temperature from $\text{35.0º C}$ to $\text{45.0º C}$ . What is the increase in entropy of the car due to this heat transfer alone?

A hot rock ejected from a volcano’s lava fountain cools from $\text{1100º C}$ to $\text{40.0º C}$ , and its entropy decreases by 950 J/K. How much heat transfer occurs from the rock?

$8.01×{\text{10}}^{5}\phantom{\rule{0.25em}{0ex}}\text{J}$

When $1\text{.}\text{60}×{\text{10}}^{5}\phantom{\rule{0.25em}{0ex}}\text{J}$ of heat transfer occurs into a meat pie initially at $\text{20.0º C}$ , its entropy increases by 480 J/K. What is its final temperature?

The Sun radiates energy at the rate of $3\text{.}\text{80}×{\text{10}}^{\text{26}}\phantom{\rule{0.25em}{0ex}}\text{W}$ from its $\text{5500º C}$ surface into dark empty space (a negligible fraction radiates onto Earth and the other planets). The effective temperature of deep space is $-\text{270º C}$ . (a) What is the increase in entropy in one day due to this heat transfer? (b) How much work is made unavailable?

(a) $1\text{.}\text{04}×{\text{10}}^{\text{31}}\phantom{\rule{0.25em}{0ex}}\text{J/K}$

(b) $3\text{.}\text{28}×{\text{10}}^{\text{31}}\phantom{\rule{0.25em}{0ex}}\text{J}$

(a) In reaching equilibrium, how much heat transfer occurs from 1.00 kg of water at $\text{40.0º C}$ when it is placed in contact with 1.00 kg of $\text{20.0º C}$ water in reaching equilibrium? (b) What is the change in entropy due to this heat transfer? (c) How much work is made unavailable, taking the lowest temperature to be $\text{20.0º C}$ ? Explicitly show how you follow the steps in the Problem-Solving Strategies for Entropy .

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

199 J/K

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

A large electrical power station generates 1000 MW of electricity with an efficiency of 35.0%. (a) Calculate the heat transfer to the power station, ${Q}_{\text{h}}$ , in one day. (b) How much heat transfer ${Q}_{\text{c}}$ occurs to the environment in one day? (c) If the heat transfer in the cooling towers is from $\text{35.0º C}$ water into the local air mass, which increases in temperature from $\text{18.0º C}$ to $\text{20.0º C}$ , what is the total increase in entropy due to this heat transfer? (d) How much energy becomes unavailable to do work because of this increase in entropy, assuming an $\text{18.0º C}$ lowest temperature? (Part of ${Q}_{\text{c}}$ could be utilized to operate heat engines or for simply heating the surroundings, but it rarely is.)

(a) $2\text{.}\text{47}×{\text{10}}^{\text{14}}\phantom{\rule{0.25em}{0ex}}\text{J}$

(b) $1\text{.}\text{60}×{\text{10}}^{\text{14}}\phantom{\rule{0.25em}{0ex}}\text{J}$

(c) $2.85×{\text{10}}^{\text{10}}\phantom{\rule{0.25em}{0ex}}\text{J/K}$

(d) $8.29×{\text{10}}^{\text{12}}\phantom{\rule{0.25em}{0ex}}\text{J}$

(a) How much heat transfer occurs from 20.0 kg of $\text{90.0º C}$ water placed in contact with 20.0 kg of $\text{10.0º C}$ water, producing a final temperature of $\text{50.0º C}$ ? (b) How much work could a Carnot engine do with this heat transfer, assuming it operates between two reservoirs at constant temperatures of $\text{90.0º C}$ and $\text{10.0º C}$ ? (c) What increase in entropy is produced by mixing 20.0 kg of $\text{90.0º C}$ water with 20.0 kg of $\text{10.0º C}$ water? (d) Calculate the amount of work made unavailable by this mixing using a low temperature of $\text{10.0º C}$ , and compare it with the work done by the Carnot engine. Explicitly show how you follow the steps in the Problem-Solving Strategies for Entropy . (e) Discuss how everyday processes make increasingly more energy unavailable to do work, as implied by this problem.

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