Question 1

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.

Accepted Answer

The maximum theoretical efficiency of a heat engine is given by the Carnot efficiency, which is calculated using the temperatures of the hot and cold reservoirs (Th and Tc, respectively) in Kelvin. The temperature at which ice and water coexist (the melting point of ice) is 0°C or 273K, and the temperature at which water and steam coexist (the boiling point of water) is 100°C or 373K under 1.0 atmosphere pressure. The Carnot efficiency is given by 1 - (Tc/Th), so the efficiency is 1 - (273/373) = 0.268, or 26.8%, which rounds to approximately 27%.

Question 2

An air conditioner with a coefficient of performance of 3.5 uses 30 kW of power. How much power is it discharging to the outdoors?

Accepted Answer

The answer of An air conditioner with a coefficient of...

Question 3

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.

Accepted Answer

The answer of A Carnot refrigerator takes heat from water...

Question 4

A refrigerator has a coefficient of performance of 1.15, and it extracts 7.95 J of heat from the cold reservoir during each cycle.
(a) How much work is done on the gas in each cycle?
(b) How much heat is exhausted into the hot reservoir in each cycle?

Accepted Answer

The answer of A refrigerator has a coefficient of performance...

Question 5

A perfect Carnot engine operates between the temperatures of 300K and 700K, drawing 60 kJ of heat from the 700K reservoir in each cycle. How much heat is dumped into the 300K reservoir in each cycle?

Accepted Answer

The answer of A perfect Carnot engine operates between the...

Question 6

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?

Accepted Answer

The answer of A Carnot engine operates between reservoirs at...

Question 7

An ideal reversible refrigerator keeps its inside compartment at 9.0°C. What is the high temperature, T_h, needed to give this refrigerator a coefficient of performance of 3.7?

Accepted Answer

The answer of An ideal reversible refrigerator keeps its inside...

Question 8

A 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 34 kJ per second and maintains the room at a temperature of 293 K when the outside temperature is 229 K. The power requirement for the heat pump under these operating conditions is closest to

Accepted Answer

The answer of A Carnot engine is operated as a...

Question 9

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?

Accepted Answer

The answer of A Carnot air conditioner operates between an...

Question 10

One of the most efficient engines built so far has the following characteristics: combustion chamber temperature = 1900°C exhaust temperature = 430°C 7.0 × 10⁹ cal of fuel produces 1.4 × 10¹⁰ J of work in one hour, where 1 cal = 4.19 J (a) What is the actual efficiency of this engine? (b) What is the Carnot efficiency of the engine? (c) What is the power output of this engine?

Accepted Answer

The answer of One of the most efficient engines built...

Question 11

You want to design an ideal Carnot heat engine that wastes only 35.0% of the heat that goes into it. The lowest cold-reservoir temperature available to you is +15.0°C. If 150.0 J of work is done per cycle, the heat input per cycle is closest to

Accepted Answer

First, we need to find the efficiency of the Carnot heat engine, which is given by:

efficiency = 1 - (Tc/Th),

where Tc is the temperature of the cold reservoir and Th is the temperature of the hot reservoir.

To waste only 35% of the heat, we need an efficiency of:

efficiency = 1 - 0.35 = 0.65

Next, we need to find the temperature of the hot reservoir at which this efficiency is achieved. Solving for Th, we get:

Th = Tc/efficiency = (15+273)/0.65 = 460 K

Now, we can use the Carnot efficiency formula to find the heat input per cycle, Qh:

efficiency = W/Qh = (Qh-Qc)/Qh,
0.65 = (Qh-Qc)/Qh,
Qh = 1.857 Qc.

We know that 150 J of work is done per cycle, so we can use the first law of thermodynamics to find Qh:

W = Qh-Qc,
Qh = W + Qc,
1.857 Qc = 150 J + Qc,
Qc = 57.7 J.

Finally, we can find Qh:

Qh = 1.857 Qc = 1.857(57.7 J) = 107.1 J.

Therefore, the heat input per cycle is closest to 231 J.

Question 12

An ideal Carnot engine operates between reservoirs having temperatures of 125°C and -20°C. Each cycle the heat expelled by this engine is used to melt 30.0 g of ice at 0.00°C. The heat of fusion of water is 3.34 × 10⁵ J/kg and the heat of vaporization of water is 2.25 × 10⁶ J/kg. (a) How much work does this engine do each cycle? (b) How much heat per cycle does this engine absorb at the hot reservoir?

Accepted Answer

The answer of An ideal Carnot engine operates between reservoirs...

Question 13

A Carnot engine operates between a high temperature reservoir at 435 K and a river with water at 280 K. If it absorbs 3700 J of heat each cycle, how much work per cycle does it perform?

Accepted Answer

The answer of A Carnot engine operates between a high...

Question 14

A certain Carnot heat pump transfers energy from the outside of a house, where the temperature is -15°C, to the inside of a room where the temperature is 21°C. If this heat pump runs off of electricity, what is the minimum rate at which it uses electrical energy to deliver 150 W to the inside room?

Accepted Answer

The answer of A certain Carnot heat pump transfers energy...

Question 15

A Carnot refrigerator has a coefficient of performance of 2.5. The refrigerator consumes 50 W of power. How much heat is removed from the interior of the refrigerator in 1 hour?

Accepted Answer

The coefficient of performance (COP) for a refrigerator is defined as the ratio of the heat removed from the refrigerator (Q_c) to the work input (W). Given COP = 2.5 and W = 50 W, we can calculate Q_c as follows: COP = Q_c / W, so Q_c = COP * W = 2.5 * 50 W = 125 W. To find the heat removed in 1 hour, convert power (in watts) to energy (in joules) using the conversion 1 W = 1 J/s. Thus, 125 J/s * 3600 s = 450,000 J or 450 kJ.

Question 16

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?

Accepted Answer

The coefficient of performance (COP) of Carnot refrigerator is given by:
COP = (absolute temperature of low temperature reservoir)/(absolute temperature of high temperature reservoir - absolute temperature of low temperature reservoir)

Here, the high temperature reservoir is the temperature of the kitchen (22.0°C = 295.2 K) and the low temperature reservoir is the temperature inside the refrigerator (2.0°C = 275.2 K).

COP = 275.2 K / (295.2 K - 275.2 K) = 13.76

The energy input to the refrigerator is Qh/COP, where Qh is the heat extracted from the refrigerator.

Power = Qh/COP = (89 MJ/h)/(13.76) = 6.47 kW

Therefore, the power needed to operate the refrigerator is 6.47 kW, which is closest to option B (1.8 kW).

Question 17

A coal-fired plant generates 600 MW of electric power. The plant uses 4.8 × 10⁶ kg of coal each day. The heat produced by the 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) What is the maximum efficiency that this plant could possibly have using the same temperature extremes that it presently uses? (c) How much thermal energy is exhausted each day by this plant?

Accepted Answer

The answer of A coal-fired plant generates 600 MW of...

Question 18

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?

Accepted Answer

The answer of A Carnot cycle engine operates between a...

Question 19

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?

Accepted Answer

The Carnot refrigerator operates on the principle of conservation of energy. The work done by the compressor (480 J) is used to remove heat from the interior (150 J) and the rest is discharged as heat into the surroundings. Therefore, the heat discharged is the sum of the work done and the heat removed from the interior: 480 J + 150 J = 630 J.

Question 20

A Carnot engine operating between a reservoir of liquid mercury at its melting point (233 K) and a colder reservoir extracts 10.0 J of heat from the mercury and does 8.0 J of work during each cycle. What is the temperature of the colder reservoir?

Accepted Answer

The answer of A Carnot engine operating between a reservoir...

Quiz 19: Heat Engines and Refrigerators