Exam 11: Using Energy

An inventor tries to sell you his new heat engine that takes in 40 J of heat at 87°C on each cycle, expels 30 J at 27°C, and does 10 J of work. Would it be wise to invest in this engine? Back up your conclusion with numerical calculations.

An ideal gas undergoes the process a→b→c→a shown in the pV diagram. In the figure, P_a = P_c = 240 kPa, V_b = V_c = 40 L, V_a = 15 L, and P_b = 400 kPa. How much heat is gained by the gas in this a→b→c→a process?

An ideal Carnot engine operates between a high temperature reservoir at $492 \mathrm {~K}$ and a river with water at $290 \mathrm {~K}$ If it absorbs $4000 \mathrm {~J}$ of heat each cycle, how much work per cycle does it perform?

An athlete doing push-ups performs 650 kJ of work and loses 425 kJ of heat. What is the change in the internal (thermal) energy of the athlete?

The figure shows a pV diagram of a gas for a complete cycle. During part bc of the cycle, 1190 J of heat flows into a system, and at the same time the system expands against a constant external pressure of $7.00 \times 10^4 \mathrm {~Pa}$ as its volume increases from $0.0200 \mathrm {~m} ^ { 3 }$ to $0.0800 \mathrm {~m} ^ { 3 }$ Calculate the change in internal (thermal) energy of the system during part bc of the cycle. If the change is nonzero, be sure to indicate whether the change is positive or negative.

A heat engine having the maximum possible efficiency has an efficiency of 35.0% when operating between two heat reservoirs. If the temperature of the hot reservoir is 700 K, what is the temperature of the cold reservoir?

Express -40°C in °F.

The weather outside is frightful. The temperature is -22°F. What is the corresponding temperature in the Celsius scale?

The ocean thermal energy conversion project uses the surface water near tropical islands with a temperature of 20°C as the hot temperature reservoir, and the water at some depth, with a temperature of 5.0°C, as the cold temperature reservoir for a heat engine. What is the maximum possible efficiency of an engine running between those two temperatures?

A Carnot air conditioner has a coefficient of performance of 17.0 and removes 72.0 MJ of heat from the interior of a house every hour. How much power does it consume?

One of the most efficient engines built so far has the following characteristics: The combustion chamber temperature is 1900°C, the exhaust temperature = 430°C, 7.0 × 10⁹ cal of fuel produces 1.4 × 10¹⁰ J of work in one hour. (1 cal = 4.186 J) (a) What is the actual efficiency of this engine? (b) What is the power output of this engine? (c) What would be the maximum possible efficiency for an engine using the same temperature extremes?

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 $11.0 \%$ What is the temperature of the warm reservoir?

A cylinder contains 10 moles of an ideal gas at a temperature of 300 K. The gas is compressed at constant pressure until the final volume equals 0.77 times the initial volume. The molar heat capacity at constant volume of the gas is 24.0 J/mol ∙ K and R = 8.31 J/mol ∙ K . How much heat is absorbed by the gas during this process? (R = 8.31 J/mol ∙ K)

A person running in place on an exercise machine for 10 min uses up 17 kcal (food calories). Another person exercises by repeatedly lifting two 2.5-kg weights a distance of 50 cm. How many repetitions of this exercise are equivalent to 10 minutes of running in place? Assume that the person uses negligible energy in letting down the weights after each lift. (1 cal = 4.186 J)

An external heat source supplies heat to a system at a rate of 187 W as the system does work at a rate of 131 W. At what rate is the internal (thermal) energy of the system changing?

An air conditioner with a coefficient of performance of 3.50 uses 30.0 kW of power to operate. What power is it discharging to the outdoors?

A person consumes a snack containing 14 food calories (14 kcal). What is the power this food produces if it is to be "burned off" due to exercise in 6 hours? (1 cal = 4.186 J)

Platinum melts at 3215°F. What is the corresponding temperature in the Kelvin scale?

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

A cylinder contains 13 moles of an ideal gas at a temperature of 300 K. The gas is compressed at constant pressure until the final volume equal 0.70 times the initial volume. The molar heat capacity at constant volume of the gas is 24.0 J/mol ∙ K. What is the change in the internal (thermal) energy of the gas during this process? (R = 8.31 J/mol ∙ K)