Exam 11: Using Energy

An ideal Carnot engine is operated as a heat pump to heat a room in the winter. The heat pump delivers heat to the room at the rate of 47 kJ per second and maintains the room at a temperature of 293 K when the outside temperature is 237 K. The power requirement to run the heat pump under these operating conditions is closest to

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?

A real (non-Carnot) heat engine, operating between heat reservoirs at temperatures of 450 K and 270 K, performs 3.3 kJ of net work, and rejects 8.2 kJ of heat in a single cycle. (a) What is the thermal efficiency of this heat engine? (b) What is the maximum efficiency it could possibly have?

A compression, at a constant pressure of 140 kPa, is performed on 4.0 moles of an ideal monatomic gas for which C_V = 3/2 R. The compression reduces the volume of the gas from $0.26 \mathrm {~m} ^ { 3 }$ to $0.12 \mathrm {~m} ^ { 3 }$ What is the change in the internal (thermal) energy of the gas during this process? (R = 8.31 J/mol ∙ K)

A cylinder contains 1.50 moles of an ideal monatomic gas that is initially at a temperature of 317 K. If the gas gains 2730 J of heat and performs 780 J of work, what is its final temperature? (R = 8.31 J/mol ∙ K)

Which two temperature changes are equivalent?

When water at 0°C freezes, the entropy of the water

An expansion process on an ideal diatomic ideal gas for which C_V = 5/2 R has a linear path between the initial and final coordinates on a pV diagram. The coordinates of the initial state are: the pressure is $300 \mathrm { kPa }$ the volume is $0.030 \mathrm {~m} ^ { 3 }$ and the temperature is $390 \mathrm {~K}$ The final pressure is $150 \mathrm { kPa }$ and the final temperature is $340 \mathrm {~K}$ What is the change in the internal (thermal) energy of the gas, during this process? (R = 8.31 J/mol ∙ K)

An ideal gas undergoes the process a→b→c→a shown in the pV diagram. The heat gained by the gas in process a→b is 546 J, while in process $b \rightarrow \mathrm { c }$ the gas loses 62.0 J of heat. In process a→b the gas performs $310 \mathrm {~J}$ of work, while in process c→a 223 J of work is done on the gas. How much heat is gained by the gas in process c→a?

A heat pump with a performance coefficient (COP) of 4.9 absorbs heat from the atmosphere at a rate of $29 \mathrm {~kW} \text {. }$ At what rate is work being done to run this heat pump?

An important feature of the Carnot cycle is that

What is absolute zero on the (a) Celsius scale and (b) on the Fahrenheit scale?

An expandable container holds 2.30 mole of helium, He, gas with an initial pressure of 770 kPa and an initial volume of 2.10 L. The gas expands isothermally to a final pressure of 350 kPa. How much heat is gained by the gas during this process? (R = 8.31 J/mol ∙ K)

A nuclear power plant has an actual efficiency of 33%. If $0.19 \mathrm { MW }$ of energy are released from fission, how much electric power does the power plant produce?

A coal-fired plant generates 600 MW of electric power. The plant uses 4.8 × 10⁶ kg of coal each day, and the heat of combustion of coal is 3.3 × 10⁷ J/kg. The steam that drives the turbines is at a temperature of 300°C, and the exhaust water is at 37°C. (a) What is the overall efficiency of the plant for generating electric power? (b) How much thermal energy is exhausted each day? (c) Using the same heat reservoirs, what is the maximum possible efficiency for a heat engine?

A 40.0-L container is divided into two equal parts by a rubber membrane. One half of the container has 1.50 moles of an ideal monatomic gas at 250 K, and the other half is a vacuum. The container is well insulated, so there is no exchange of heat with the surroundings. The membrane breaks, and eventually the gas reaches a new equilibrium condition occupying the entire volume. What is the final temperature of the gas?

An ideal Carnot heat engine operates between reservoirs at 1740 K and $150 \mathrm {~K}$ 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?

A heat engine with an efficiency of 30% performs 2500 J of work. How much heat is discharged to the lower temperature reservoir?

During each cycle, a refrigerator removes 20.0 kJ of heat from the freezing compartment and ejects 24.0 kJ into a room. (a) How much work per cycle is required each cycle to run this refrigerator? (b) What is the coefficient of performance of this refrigerator?

A heat engine has an efficiency of 31.4% and receives 8.72 kJ of heat per cycle. (a) How much work does it perform in each cycle? (b) How much heat does it exhaust in each cycle?