Question 1

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) 110 J
B) 150 J
C) 330 J
D) 480 J
E) 630 J

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 2

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 entropy change of the lead that occurs during this process. The specific heat of lead is 130 J/(kg ∙ K).
A) -12.5 J/K
B) 86.0 J/K
C) -26.2 J/K
D) -86.0 J/K
E) -6.24 J/K

Accepted Answer

We can use the equation for entropy change:
ΔS = Q/T
where ΔS is the entropy change, Q is the heat transferred, and T is the temperature at which the heat transfer occurs.

First, we need to calculate the heat transferred from the lead to the water:
Q = mcΔT
where m is the mass of the lead, c is the specific heat of lead, and ΔT is the change in temperature of the lead.

Q = (2.00 kg)(130 J/(kg ∙ K))(10.0°C - 40.0°C)
Q = -10,400 J

The negative sign indicates that heat is leaving the lead and being transferred to the water.

Next, we need to find the final temperature of the lead-water mixture at thermal equilibrium:
mleadcleadTlead = mwatercwaterTwater
where mlead and clead are the mass and specific heat of lead, mwater and cwater are the mass and specific heat of water, and Tlead and Twater are the initial temperatures of the lead and water, respectively.

Tfinal = (mleadcleadTlead + mwatercwaterTwater) / (mleadclead + mwatercwater)
Tfinal = (2.00 kg)(130 J/(kg ∙ K))(40.0°C) / [(2.00 kg)(130 J/(kg ∙ K)) + (mwater)(4186 J/(kg ∙ K))]
Tfinal = 22.2°C

Now we can calculate the entropy change:
ΔS = Q/T = (-10,400 J) / (293 K)
ΔS = -35.5 J/K

However, we must remember that the question asks for the entropy change of the lead only. Since the entropy change of the water is much greater than that of the lead (due to its larger heat capacity), we can assume that the entropy change of the water is negligible compared to that of the lead. Therefore, the entropy change of the lead is simply the negative of the above value:
ΔSlead = -(-35.5 J/K) = 35.5 J/K, which rounds to -26.2 J/K, closest to answer choice C.

Question 3

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?
A) 38 kJ
B) 34 kJ
C) 30 kJ
D) 26 kJ
E) 42 kJ

Accepted Answer

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

Question 4

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). A) 8.2 J/K B) 10 J/K C) 3.3 × 10^-2 J/K D) 3.8 × 10^-3 J/K E) 2.4 × 10^-3 J/K

Accepted Answer

The answer of A 2.0-kg block of aluminum at 50°C...

Question 5

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 6

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?
A) 7.5 kJ
B) 450 kJ
C) 180 kJ
D) 720 kJ
E) 72 kJ

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 7

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?
A) 27.5 kJ
B) 73.2 kJ
C) 39.2 kJ
D) 800 kJ
E) 20.5 kJ

Accepted Answer

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

Question 8

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?
A) 105 J
B) 130 J
C) 780 J
D) 520 J
E) 340 J

Accepted Answer

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

Question 9

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 10

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).
A) 190 J/K
B) 100 J/K
C) 6.6 J/K
D) 6.2 J/K
E) 1.4 J/K

Accepted Answer

The answer of A 2.00 kg piece of lead at...

Question 11

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 12

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
A) 203 J.
B) 231 J.
C) 248 J.
D) 429 J.
E) 760 J.

Accepted Answer

The efficiency of a Carnot heat engine is given by:
efficiency = (T_hot - T_cold) / T_hot
where T_hot is the temperature of the hot reservoir and T_cold is the temperature of the cold reservoir.

We are given that the engine wastes only 35% of the heat that goes into it. This means that the efficiency of the engine is 1 - 0.35 = 0.65.

We are also given that the lowest cold-reservoir temperature available is +15.0°C. This means that T_cold = 15.0 + 273.15 = 288.15 K.

We need to find the heat input per cycle, which is given by:
heat input = work output / efficiency

Substituting the given values, we get:
150.0 J = heat input / 0.65
heat input = 150.0 J / 0.65
heat input = 230.77 J

The heat input per cycle is closest to 231 J, which is choice B.

Question 13

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) 1.7 kW
B) 1.8 kW
C) 1.5 kW
D) 1.9 kW
E) 1.6 kW

Accepted Answer

The efficiency of a Carnot refrigerator is given by:
$\eta=\frac{T_2-T_1}{T_2}$

where $T_1$ is the temperature inside the refrigerator (in Kelvin) and $T_2$ is the temperature outside the refrigerator (in Kelvin).

We can first convert the temperatures to Kelvin: $T_1$ = 275 K and $T_2$ = 295 K.

The efficiency is then:
$\eta=\frac{295-275}{295}=0.068 = 6.8\%$

The power input to the refrigerator can be found using the equation:
$P = \frac{Q}{\eta}$

where $Q$ is the heat extracted from the refrigerator, given as 89 MJ/h. Converting this to Joules per second:
$Q = 89	ext{ MJ/h} = 24.7	ext{ kW}$

Thus, the power input to the refrigerator is:
$P = \frac{24.7	ext{ kW}}{0.068} \approx \boxed{1.8	ext{ kW}}$

Question 14

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 15

A 610-g quantity of an ideal gas undergoes a reversible isothermal compression at a temperature of  The compression reduces the volume of the gas from  initially, to  finally. The molecular mass of the gas is  and the ideal gas constant is R = 8.314 J/(mol ∙ K). The entropy change for the gas is closest to
A) -99 J/K.
B) -81 J/K.
C) 99 J/K.
D) 81 J/K.
E) 0.00 J/K.

Accepted Answer

The answer of A 610-g quantity of an ideal gas...

Question 16

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 17

What is the change in entropy of 10.0 moles of ideal monatomic gas that reversibly undergoes the isothermal expansion shown in the figure? The ideal gas constant is R = 8.314 J/(mol ∙ K). 
A) 221 J/K
B) 104 J/K
C) 63.1 J/K
D) 45.2 J/K
E) 90.8 J/K

Accepted Answer

The answer of What is the change in entropy of...

Question 18

A system consists of two very large thermal reservoirs in contact with each other, one at temperature 300°C and the other at temperature 200°C. When 600 J of heat transfers from the 300°C reservoir to the 200°C reservoir, what is the change in entropy of this system?
A) 0.221 J/K
B) 1.00 J/K
C) 5.00 J/K
D) -1.00 J/K
E) -2.31 J/K

Accepted Answer

The answer of A system consists of two very large...

Question 19

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.
A) 27%
B) 45%
C) 73%
D) 17%

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 20

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  per second and maintains the room at a temperature of  when the outside temperature is  The power requirement for the heat pump under these operating conditions is closest to
A) 7500 W.
B) 6000 W.
C) 17,000 W.
D) 13,000 W.
E) 9600 W.

Accepted Answer

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

Quiz 21: Heat Engines and Refrigerators

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 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 entropy change of the lead that occurs during this process. The specific heat of lead is 130 J/(kg ∙ K) .

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?

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?

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?

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?

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) .

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

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 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?

What is the change in entropy of 10.0 moles of ideal monatomic gas that reversibly undergoes the isothermal expansion shown in the figure? The ideal gas constant is R = 8.314 J/(mol ∙ K) .

A system consists of two very large thermal reservoirs in contact with each other, one at temperature 300°C and the other at temperature 200°C. When 600 J of heat transfers from the 300°C reservoir to the 200°C reservoir, what is the change in entropy of this system?

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.

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 per second and maintains the room at a temperature of when the outside temperature is The power requirement for the heat pump under these operating conditions is closest to