Chapter 11

Follow-up After walking for a few minutes, you begin to run, doing \(5.1 \times 10^{5} \mathrm{~J}\) of work and decreasing your thermal energy by \(8.8 \times 10^{5} \mathrm{~J}\). How much heat did you give off while running?

A swimmer does \(4.3 \times 10^{5} \mathrm{~J}\) of work and gives off \(1.7 \times 10^{5} \mathrm{~J}\) of heat during a workout. Determine \(\Delta E, W\), and \(Q\) for the swimmer.

Give the change in thermal energy of a system if (a) \(W=50 \mathrm{~J}, Q=50 \mathrm{~J}\); (b) \(W=-50 \mathrm{~J}, Q=-50 \mathrm{~J}\); or (c) \(W=50 \mathrm{~J}, Q=-50 \mathrm{~J}\).

Follow-up What is the efficiency of a heat engine that does \(1250 \mathrm{~J}\) of work and gives off \(5250 \mathrm{~J}\) of heat to the cold reservoir?

What is the efficiency of an engine that exhausts \(870 \mathrm{~J}\) of heat in the process of doing \(340 \mathrm{~J}\) of work?

An engine receives \(690 \mathrm{~J}\) of heat from a hot reservoir and gives off \(430 \mathrm{~J}\) of heat to a cold reservoir. What are (a) the work done by the engine and (b) the efficiency of the engine?

Explain How does the first law of thermodynamics extend the principle of conservation of energy?

Describe How does the energy of a heat engine change as it goes through one cycle?

Assess Which of the following indicates that the efficiency of a heat engine has increased? Explain your reasoning. Case A: Adding more heat to the engine produces the same amount of work. Case B: Adding the same amount of heat to the engine produces more work.

Big Idea If an object slides across a floor and comes to rest, what has become of its kinetic energy? Is this a violation of energy conservation? Solving Problems

If an object slides across a floor and comes to rest, what has become of its kinetic energy? Is this a violation of energy conservation? Solving Problems

Rank Determine the thermal energy changes of systems A through D, described below, and then rank them in order of increasing change in thermal energy. Indicate ties where appropriate. $$ \begin{array}{|c|c|c|c|c|} \hline \text { System } & \mathbf{A} & \mathbf{B} & \mathbf{C} & \mathbf{D} \\\ \hline \boldsymbol{W}(\boldsymbol{J}) & 10 & -10 & 30 & -20 \\ \hline \boldsymbol{Q}(\boldsymbol{J}) & 20 & -20 & -50 & -10 \\ \hline \end{array} $$

Rank Determine the efficiencies of the engines \(\mathrm{A}\) through D, described below, and then rank them in order of increasing efficiency. Indicate ties where appropriate. \begin{tabular}{|c|c|c|c|c|} \hline Engine & A & B & C & D \\ \hline \(\mathbf{Q}_{\mathbf{h}}(\mathbf{J})\) & 40 & 140 & 80 & 240 \\ \hline \(\mathbf{Q}_{\mathbf{c}}(\mathbf{J})\) & 20 & 120 & 40 & 220 \\ \hline \end{tabular}

Rank Determine the efficiencies of the engines A through D, described below, and then rank them in order of increasing efficiency. Indicate ties where appropriate. $$ \begin{array}{|c|c|c|c|c|} \hline \text { Engine } & \mathbf{A} & \mathbf{B} & \mathbf{C} & \mathbf{D} \\\ \hline \mathbf{Q}_{\mathbf{h}}(\mathbf{J}) & 40 & 140 & 80 & 240 \\ \hline \mathbf{Q}_{\mathbf{c}}(\mathbf{J}) & 20 & 120 & 40 & 220 \\ \hline \end{array} $$

Calculate A system's thermal energy decreases by \(20 \mathrm{~J}\) while the system performs \(10 \mathrm{~J}\) of work. How much heat was added to the system?

Calculate A gas does \(100 \mathrm{~J}\) of work as it expands. How much heat must be added to this gas for its thermal energy to decrease by \(40 \mathrm{~J}\) ?

Calculate A heat engine takes in \(1220 \mathrm{~J}\) of heat from the hot reservoir and exhausts \(680 \mathrm{~J}\) of heat to the cold reservoir. (a) How much work is done by the engine? (b) What is the efficiency of the heat engine?

As a gas expands at constant pressure from a volume of \(0.74 \mathrm{~m}^{3}\) to a volume of \(2.3 \mathrm{~m}^{3}\), it does \(93 \mathrm{~J}\) of work. What is the pressure of the gas during this process?

A gas with a constant pressure of \(270 \mathrm{kPa}\) does \(36,000 \mathrm{~J}\) of work as it expands. What was the change in volume of the gas?

Follow-up If a system's thermal energy decreases by \(470 \mathrm{~J}\) in an adiabatic process, how much work was done by the system?

A gas expands adiabatically and does \(520 \mathrm{~J}\) of work. What is the change in thermal energy of the gas?

Scrutinize State whether each of the following statements is true or false. If a statement is false, revise it so that it becomes true. (a) The change in thermal energy in a constant-volume process is zero. (b) The work done in a constant-pressure process is zero. (c) The area under the curve on a pressure-volume graph is equal to the work. (d) Work and heat are equal in an isothermal process. (e) The thermal energy of a system increases when work is done on it in an adiabatic process.

Assess The temperature of a system is held fixed. Is it possible for thermal energy to flow into the system? Give an explanation if your answer is no. If your answer is yes, give a specific example.

Relate How is the change in thermal energy related to the work in an adiabatic process?

Triple Choice A gas does \(50 \mathrm{~J}\) of work as it expands adiabatically. Is the change in thermal energy of this gas \(50 \mathrm{~J}, 0 \mathrm{~J}\), or \(-50 \mathrm{~J}\) ? Explain.

Calculate How much heat must be added to a gas that does \(10 \mathrm{~J}\) of work in a constant-temperature (isothermal) process?

Calculate An ideal gas is compressed at a constant pressure of \(120 \mathrm{kPa}\) to one-half of its initial volume. The work done on the gas is \(790 \mathrm{~J}\). What was the initial volume of the gas?

Heat is added to a \(0.14-\mathrm{kg}\) block of ice at \(0^{\circ} \mathrm{C}\), increasing its entropy by \(98 \mathrm{~J} / \mathrm{K}\). How much ice melts?

\(\square\) Identify Which law of thermodynamics says that thermal energy flows from hot objects to cold objects?

Identify Which law of thermodynamics says that thermal energy flows from hot objects to cold objects?

Explain What does Carnot's theorem say about the feasibility of a 100\% efficient heat engine?

The molecules in ice are in a more orderly and structured state than the molecules in liquid water. Does freezing water to form ice decrease the entropy of the universe?

Explain If the entropy of a system increases, what can you say about its randomness?

Decide Which has more entropy: (a) popcorn kernels or the resulting popcorn, (b) two eggs in a carton or an omelet made from the eggs, (c) a pile of bricks or a house made from them, (d) a piece of paper or the ash after the paper has been burned?

Rank The reservoir temperatures for heat engines A through D are given below. Rank the engines in order of increasing efficiency. Indicate ties where appropriate. \begin{tabular}{|c|c|c|c|c|} \hline Engine & \(\mathbf{A}\) & \(\mathbf{B}\) & \(\mathbf{C}\) & D \\ \hline \(\boldsymbol{T}_{\mathbf{h}}(\mathbf{K})\) & 400 & 440 & 800 & 1240 \\ \hline \(\boldsymbol{T}_{\mathbf{C}} \mathbf{( K )}\) & 200 & 420 & 600 & 1020 \\\ \hline \end{tabular}

Calculate A heat engine has a high-temperature reservoir at \(330 \mathrm{~K}\) and a low-temperature reservoir at \(260 \mathrm{~K}\). What is the maximum efficiency of this engine?

Calculate A heat engine has a high-temperature reservoir at \(410 \mathrm{~K}\) and operates at a maximum efficiency of \(0.24\). What is the temperature of this engine's low-temperature reservoir?

Calculate What is the efficiency of a heat engine that exhausts \(870 \mathrm{~J}\) of heat in the process of doing \(340 \mathrm{~J}\) of work?

Calculate An ideal heat engine operates between the temperatures \(390 \mathrm{~K}\) and \(240 \mathrm{~K}\). (a) How much heat must be given to the engine to produce 1200 J of work? (b) How much heat is discarded to the cold reservoir as this work is done?

Calculate Determine the change in entropy that occurs when \(3.1 \mathrm{~kg}\) of water freezes at \(0^{\circ} \mathrm{C}\).

Why do heat and work have opposite signs in the equation \(\Delta E=Q-W\) ?

A system receives \(100 \mathrm{~J}\) of heat. If the thermal energy of the system remains constant, how much work does the system do?

Engine 1 takes in \(100 \mathrm{~J}\) of heat from a hot reservoir and does \(20 \mathrm{~J}\) of work. Engine 2 takes in the same amount of heat from the hot reservoir and does \(25 \mathrm{~J}\) of work. Is the efficiency of engine 1 greater than, less than, or equal to the efficiency of engine 2? Explain.

Engine 1 takes in \(100 \mathrm{~J}\) of heat from a hot reservoir and does \(20 \mathrm{~J}\) of work. Engine 2 takes in \(600 \mathrm{~J}\) of heat from the hot reservoir and does \(60 \mathrm{~J}\) of work. Is the efficiency of engine 1 greater than, less than, or equal to the efficiency of engine 2 ?

Find the heat associated with each of the following processes: (a) \(W=50 \mathrm{~J}, \Delta E=50 \mathrm{~J}\); (b) \(W=-50 \mathrm{~J}\), \(\Delta E=-50 \mathrm{~J}\); (c) \(W=50 \mathrm{~J}, \Delta E=150 \mathrm{~J}\).

An engine receives \(770 \mathrm{~J}\) of heat from a hot reservoir and does \(160 \mathrm{~J}\) of work. What is (a) the efficiency of this engine and (b) the heat given off to the cold reservoir?

What is the efficiency of an engine that exhausts \(440 \mathrm{~J}\) of heat to a cold reservoir and receives \(570 \mathrm{~J}\) of heat from a hot reservoir?

A basketball player does \(2.43 \times 10^{5} \mathrm{~J}\) of work during her time in the game, and \(0.110 \mathrm{~kg}\) of water evaporates from her skin. Assuming a latent heat of \(2.26 \times 10^{6} \mathrm{~J} / \mathrm{kg}\) for the evaporation of sweat (the same as for water), determine the change in the player's thermal energy.

Three different processes act on a system. (a) In process A , \(42 \mathrm{~J}\) of work are done on the system and \(77 \mathrm{~J}\) of heat are added to the system. Find the change in the system's thermal energy. (b) In process \(B\), the system does \(42 \mathrm{~J}\) of work and \(77 \mathrm{~J}\) of heat are added to the system. What is the change in the system's thermal energy? (c) In process \(\mathrm{C}\), the system's thermal energy decreases by \(120 \mathrm{~J}\) while the system performs \(120 \mathrm{~J}\) of work on its surroundings. How much heat was added to the system?

Which of the physical quantities, \(Q, W\), or \(\Delta E\), is zero in a constant-volume process?