Exam 15: The Laws of Thermodynamics

An ideal Carnot refrigerator with a performance coefficient (COP) of $5.0$ cools items inside of it to $5.0 ^ { \circ } \mathrm { C }$ . What is the high temperature needed to operate this refrigerator?

An ideal Carnot engine operating between a warm reservoir of unknown temperature and a cold reservoir at $1.76 \mathrm {~K}$ has an efficiency of $40.0 \%$ . What is the temperature of the warm reservoir?

The figure shows a $p V$ diagram for $2.9 \mathrm {~g}$ of ideal oxygen gas $\mathrm { O } _ { 2 }$ in a sealed container. The temperature of state 1 is $76 ^ { \circ } \mathrm { C }$ , the atomic mass of the oxygen atom is $16 \mathrm {~g} / \mathrm { mol }$ , and $R = 8.31 \mathrm {~J} / \mathrm { mol }$ -K. What are the temperatures $T _ { 3 }$ and $T _ { 4 }$ ?

An ideal Carnot heat engine operates between reservoirs at 1740 K and 150 K. In each cycle, 260 J of heat energy is rejected to the low temperature reservoir. In each cycle, how much mechanical work W is performed by the engine?

If the efficiency of a reversible engine is 28%, what is its COP (performance coefficient) operated (a) as a refrigerator, and (b) as a heat pump?

What is the change in entropy of the lead when $2.0 \mathrm {~kg}$ of molten lead at its melting point temperature solidifies? For lead: $L _ { V } = 207 \mathrm { kcal } / \mathrm { kg }$ at $1744 ^ { \circ } \mathrm { C } , L F = 5.9 \mathrm { kcal } / \mathrm { kg }$ at $328 ^ { \circ } \mathrm { C }$ .

A 15.0-kg block of ice at 0.00°C falls into Lake Superior, which is a fresh water lake. The lake water is at 10.0°C, and the latent heat of fusion for ice is 3.34 × 105 J/kg. Find the change in entropy due to the melting of the ice (a) of the block of ice, (b) of the lake, and (c) of the system consisting of the lake and the ice. (d) Is your answer to part (c) consistent with the reversibility or irreversibility of the melting process?

On a cold winter day, the outside temperature is $- 20 ^ { \circ } \mathrm { C }$ and the inside temperature is maintained at $20 ^ { \circ } \mathrm { C }$ . There is a net heat flow to the outside through the walls, roof, etc., of $25 \mathrm {~kW}$ . What is the rate of increase of the entropy of the universe as a result of this heat flow?

An ideal Carnot refrigerator powered from an electrical outlet takes heat from water at $0.0 ^ { \circ } \mathrm { C }$ and rejects heat to a room at $20.0 ^ { \circ } \mathrm { C }$ . How much electrical energy must be supplied to the refrigerator so it will convert $78 \mathrm {~g}$ of water at $0.0 ^ { \circ } \mathrm { C }$ to ice at $0.0 ^ { \circ } \mathrm { C }$ . The latent heat of fusion of water is $3.34 \times 10 ^ { 5 } \mathrm {~J} / \mathrm { kg }$ .

An expansion process on an ideal diatomic ideal gas has a linear path between the initial and final coordinates on a $p V$ diagram. The coordinates of the initial state are: the pressure is $300 \mathrm { kPa }$ , the volume is $0.0700 \mathrm {~m} ^ { 3 }$ , and the temperature is $390 \mathrm {~K}$ . The final pressure is $130 \mathrm { kPa }$ and the final temperature is $310 \mathrm {~K}$ . How much work is done by the gas during this process? $( R = 8.31 \mathrm {~J} / \mathrm { mol } \cdot \mathrm { K } )$

An ideal Carnot heat engine operates between $285 \mathrm {~K}$ and $460 \mathrm {~K}$ . What is its efficiency?

A reversible engine takes in heat at a rate of 555 W and exhausts heat at 482 W. (a) How much power does it produce? (b) What is its efficiency? (c) If operated in reverse as a refrigerator, what would be its performance coefficient (COP)?

A heat engine absorbs 85.6 kJ of heat each cycle and exhausts 61.8 kJ. (a) What is the efficiency of the engine? (b) How much work does it do each cycle?

When water at $0 ^ { \circ } \mathrm { C }$ freezes, the entropy of the water

The temperature of an ideal gas in a sealed rigid $0.20 - \mathrm { m } ^ { 3 }$ container is reduced from $360 \mathrm {~K}$ to $270 \mathrm {~K}$ , and the final pressure of the gas is 40 kPA. How much work is done by the gas during this process? $( R = 8.31 \mathrm {~J} / \mathrm { mol } \cdot \mathrm { K } )$

The process shown on the $p V$ diagram in the figure is an

Two processes are shown on the $p V$ diagram in the figure. One of them is an adiabat and the other one is an isotherm. Which process is the isotherm?

The figure shows a $p V$ diagram for an ideal gas that is carried around a cyclic process. How much work is done in one cycle if $p _ { 0 } = 4.00 \mathrm {~atm}$ and $\mathrm { V } _ { 0 } = 3.00 \mathrm {~L}$ ? $( 1.00 \mathrm {~atm} = 101 \mathrm { kPa } )$

A heat engine receives $7000 \mathrm {~J}$ of heat and loses $3000 \mathrm {~J}$ in each cycle. What is the efficiency of this engine?

The figure shows a $p V$ diagram for $2.6 \mathrm {~g}$ of ideal helium gas that undergoes the process $1 \rightarrow 2 \rightarrow 3$ . Find the value of volume $V _ { 3 }$ . The atomic mass of helium is $4.0 \mathrm {~g} / \mathrm { mol }$ , and $R = 8.31 \mathrm {~J} / \mathrm { mol } \cdot \mathrm { K }$ .