Exam 19: Heat Engines and Refrigerators

A Carnot refrigerator takes heat from water at 0°C and rejects heat to a room at 12°C. Suppose that 92.0 grams of water at 0°C are converted to ice at 0°C by the refrigerator. Calculate the mechanical energy that must be supplied to the refrigerator. The heat of fusion of water is 3.34 × 10⁵ J/kg.

What is the maximum theoretical efficiency possible for a heat engine operating between a reservoir in which ice and water coexist, and a reservoir in which water and steam coexist? The pressure is constant at 1.0 atmosphere for both reservoirs.

At atmospheric pressure, 45 moles of liquid helium are vaporized at its boiling point of 4.22 K. The heat of vaporization of helium, at atmospheric pressure, is 2.09 × 10⁴ J/kg, and the atomic weight of helium is 4.00 g/mol. The change in the entropy of the helium, as it vaporizes, is closest to

A 2.00 kg piece of lead at 40.0°C is placed in a very large quantity of water at 10.0°C, and thermal equilibrium is eventually reached. Calculate the TOTAL change in entropy that occurs during this process. The specific heat of lead is 130 J/(kg∙K).

The entropy of an isolated system must be conserved, so it never changes.

A Carnot cycle engine operates between a low temperature reservoir at 20°C and a high temperature reservoir at 800°C. If the engine is required to output 20.0 kJ of work per cycle, how much heat must the high temperature reservoir transfer to the engine during each cycle?

An automobile engine takes in 4000 J of heat and performs 1100 J of mechanical work in each cycle. (a) Calculate the engine's efficiency. (b) How much heat is "wasted" in each cycle?

A heat engine with an efficiency of 30.0% performs 2500 J of work. How much heat is discharged to the lower temperature reservoir?

An ice cube at 0°C is placed in a very large bathtub filled with water at 30°C and allowed to melt, causing no appreciable change in the temperature of the bath water. Which one of the following statements is true?

A heat engine performs the reversible cycle abca with 9.0 moles of an ideal gas, as shown in the figure. Path ca is an adiabatic process. The temperatures at points a and b are 300 K and 500 K, respectively. The volume at point c is 0.20 m³. The adiabatic constant of the gas is 1.60. The thermal efficiency of this engine is closest to

A refrigerator removes heat from the freezing compartment at the rate of 20 kJ and ejects 24 kJ into a room per cycle. How much work is required in each cycle?

Is it possible to transfer heat from a hot reservoir to a cold reservoir?

The temperature inside a Carnot refrigerator placed in a kitchen at 22.0°C is 2.0°C. The heat extracted from the refrigerator is 89 MJ/h. What power is needed to operate this refrigerator?

A 2.0-kg block of aluminum at 50°C is dropped into 5.0 kg of water at 20°C and the temperature is allowed to stabilize. What is the total change in entropy during this process, assuming no heat is exchanged with the environment? The specific heat of aluminum is 910 J/(kg∙K) and the specific heat of water is 4190 J/(kg∙K).

According to the second law of thermodynamics, the entropy of any system always increases.

A Carnot engine operates between reservoirs at 550K and 300K, discarding 1500 J of heat in each cycle. (a) What is the engine's efficiency? (b) How much heat is supplied to the engine by the hot reservoir in each cycle?

A brass rod, 75.0 cm long and having a cross-sectional area of 2.50 cm², conducts heat from a large furnace at 375°C into a very large cold water bath at 10.0°C without losing any heat at the lateral surface of the rod. Steady state has been established, and the thermal conductivity of brass is 109 W/m∙K. The rate at which the entropy of the system (furnace plus water) is changing is closest to

The compressor in a certain Carnot refrigerator performs 480 J of work to remove 150 J of heat from the interior of the refrigerator. How much heat must the coils behind the refrigerator discharge into the kitchen?

A 2.00-kg block of ice at 0.00°C is dropped into a very large lake at 25.0°C and completely melts. For water, the heat of fusion is 3.35 × 10⁵ J/kg, the heat of vaporization is 2.25 × 10⁵ J/kg, and the specific heat is 4190 J/kg∙K. The net change in entropy of the system consisting of the ice and the lake due to this melting process is closest to

A Carnot air conditioner operates between an indoor temperature of 20°C and an outdoor temperature of 39°C. How much energy does it need to remove 2000 J of heat from the interior of the house?