Question 1

A reversible engine takes in heat at a rate of 555 W and exhausts heat at 482 W.
(a)How much power does it produce?
(b)What is its efficiency?
(c)If operated in reverse as a refrigerator, what would be its performance coefficient (COP)?

Accepted Answer

The answer of A reversible engine takes in heat at...

Question 2

An ideal Carnot engine operates between a warm reservoir at 233 K and a colder reservoir. During each cycle, this engine extracts $15.0 \mathrm {~J}$ of heat from the warm reservoir and does $4.0 \mathrm {~J}$ of work. What is the temperature of the colder reservoir?
A)171 K
B)62 K
C)47 K
D)67 K

Accepted Answer

The efficiency of a Carnot engine is given by:$$e=\frac{W}{Q_H}=1-\frac{T_C}{T_H}$$where $W$ is the work done, $Q_H$ is the heat extracted from the warm reservoir, $T_C$ is the temperature of the colder reservoir, and $T_H$ is the temperature of the warm reservoir.We can rearrange this equation to solve for $T_C$:$$T_C=T_H(1-e)$$Substituting the given values, we get:$$T_C=233\mathrm{~K}(1-\frac{4.0\mathrm{~J}}{15.0\mathrm{~J}})=171\mathrm{~K}$$Therefore, the temperature of the colder reservoir is 171 K.

Question 3

Suppose that the Department of Energy develops a new reversible engine that has a coefficient of performance (COP)of 4.0 when operated as a refrigerator and a COP of 5.0 when operated as a heat pump. What is its thermal efficiency when operated as a heat engine doing work?
A)10%
B)20%
C)25%
D)45%
E)80%

Accepted Answer

The answer of Suppose that the Department of Energy develops...

Question 4

If the efficiency of a reversible engine is 28%, what is its COP (performance coefficient)operated (a)as a refrigerator, and (b)as a heat pump?

Accepted Answer

The answer of If the efficiency of a reversible engine...

Question 5

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?
A)1642 J
B)2358 J
C)1483 J
D)2517 J

Accepted Answer

The efficiency of a Carnot engine is given by:$$\eta = 1 - \frac{T_c}{T_h}$$where $T_c$ is the temperature of the cold reservoir and $T_h$ is the temperature of the hot reservoir.In this case, $T_c = 290 \mathrm {~K}$ and $T_h = 492 \mathrm {~K}$, so the efficiency is:$$\eta = 1 - \frac{290 \mathrm {~K}}{492 \mathrm {~K}} = 0.411$$The work done per cycle is given by:$$W = Q_h \eta$$where $Q_h$ is the heat absorbed per cycle.In this case, $Q_h = 4000 \mathrm {~J}$, so the work done per cycle is:$$W = 4000 \mathrm {~J} \times 0.411 = 1644 \mathrm {~J}$$Therefore, the correct answer is A.

Question 6

An ideal Carnot air conditioner operates between an indoor temperature of 20°C and an outdoor temperature of 39°C. How much energy does it use 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 An ideal Carnot air conditioner operates between...

Question 7

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 $40.0 \%$ What is the temperature of the warm reservoir?
A)2.93 K
B)0.0500 K
C)106 K
D)0.0400 K

Accepted Answer

The efficiency of a Carnot engine is given by $ \eta = 1 - \frac{T_c}{T_h} $. Given $\eta = 0.40$ and $T_c = 1.76 \, \text{K}$, solving for $T_h$ gives $T_h = \frac{T_c}{1 - \eta} = \frac{1.76}{0.60} = 2.93 \, \text{K}$.

Question 8

An ideal reversible heat pump is taking heat from the outside air at -10.0°C and discharging it into the house at 18.0°C. What is the coefficient of performance of this heat pump?
A)10.4
B)9.44
C)0.644
D)0.533
E)0.0962

Accepted Answer

The answer of An ideal reversible heat pump is taking...

Question 9

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?

Accepted Answer

The answer of During each cycle, a refrigerator removes 20.0...

Question 10

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)1.98 K
B)0.180 K
C)157 K
D)0.160 K

Accepted Answer

The efficiency of a Carnot engine is given by $ \eta = 1 - \frac{T_c}{T_h} $. Given $\eta = 0.11$ and $T_c = 1.76 \, \text{K}$, solving for $T_h$ gives $T_h = \frac{T_c}{1 - \eta} = \frac{1.76}{0.89} \approx 1.98 \, \text{K}$.

Question 11

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?

Accepted Answer

The answer of A real (non-Carnot)heat engine, operating between heat...

Question 12

A Carnot engine operates between two reservoirs with unknown temperatures. If the Carnot engine operates at $67 \%$ efficiency, what is the ratio of the absolute temperatures of the reservoirs, T_c/T_h? A)0.33 B)0.0012 C)0.0025 D)0.67

Accepted Answer

The efficiency of a Carnot engine is given by $1 - \frac{T_c}{T_h}$. If the efficiency is 67%, then $1 - \frac{T_c}{T_h} = 0.67$, which implies $\frac{T_c}{T_h} = 0.33$.

Question 13

The "hot shot" heat engine operating between 40°C and 380°C has an efficiency that is 60% of that of an ideal Carnot engine operating between the same temperatures. If the "hot shot" engine absorbs heat at a rate of 60 kW, at what rate does it exhaust heat?
A)36 kW
B)41 kW
C)57 kW
D)60 kW

Accepted Answer

The efficiency of the "hot shot" engine is 60% of that of an ideal Carnot engine operating between the same temperatures, so the efficiency of the Carnot engine can be calculated as 1.00 (100%) / 0.60 = 1.67 (167%). The efficiency of a Carnot engine is given by (Th - Tl) / Th, where Th is the absolute temperature of the hot reservoir and Tl is the absolute temperature of the cold reservoir. Therefore, the absolute temperatures of the hot and cold reservoirs for the "hot shot" engine are 40°C + 273.15 = 313.15 K and 380°C + 273.15 = 653.15 K, respectively. Using the equation for efficiency, we can find the efficiency of the "hot shot" engine as (313.15 - 653.15) / 313.15 = 0.5000 (50.00%). The ratio of the actual efficiency to the Carnot efficiency is then 0.5000 / 1.67 = 0.2994 (29.94%). This means that the "hot shot" engine exhausts 70.06% of the absorbed heat, or 60 kW x 0.7006 = 42.07 kW, which rounds to 41 kW. Therefore, the answer is (B) 41 kW.

Question 14

During each cycle of operation, a refrigerator absorbs 230 J of heat from the freezer and expels 356 J of heat to the room. How much work input is required in each cycle?
A)712 J
B)586 J
C)460 J
D)126 J

Accepted Answer

The work input required for each cycle of a refrigerator can be calculated using the first law of thermodynamics, which states that the change in the internal energy of a system is equal to the heat added to the system minus the work done by the system. In the context of a refrigerator, the work input is equal to the heat expelled to the room minus the heat absorbed from the freezer. Therefore, the work input is 356 J - 230 J = 126 J.

Question 15

A refrigerator has a performance coefficient (COP)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 performance coefficient (COP)of...

Question 16

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)30.0 kW
B)75.0 kW
C)105 kW
D)135 kW
E)210 kW

Accepted Answer

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

Question 17

A refrigerator has a coefficient of performance equal to 4.2. How much work must be done on the operating gas in the refrigerator in order to remove 250 J of heat from the interior compartment?
A)60 J
B)120 J
C)250 J
D)480 J
E)1050 J

Accepted Answer

The coefficient of performance (COP) for a refrigerator is given by COP = Qc/W, where Qc is the heat removed from the cold reservoir (interior compartment) and W is the work done on the system. Given COP = 4.2 and Qc = 250 J, we can rearrange the formula to solve for W: W = Qc / COP = 250 J / 4.2 ≈ 60 J.

Question 18

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.

Accepted Answer

The answer of An inventor tries to sell you his...

Question 19

During each cycle, the compressor in a certain ideal Carnot refrigerator performs 480 J of work to remove 150 J of heat from the interior of the refrigerator. How much heat do the coils behind the refrigerator discharge into the kitchen each cycle?
A)110 J
B)150 J
C)330 J
D)480 J
E)630 J

Accepted Answer

The answer of During each cycle, the compressor in a...

Question 20

What is the efficiency of an ideal Carnot 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 atm for both reservoirs.
A)27%
B)0.27%
C)100%
D)1.0%
E)15%

Accepted Answer

The efficiency ($\eta$) of an ideal Carnot engine is given by $\eta = 1 - \frac{T_C}{T_H}$, where $T_C$ and $T_H$ are the temperatures of the cold and hot reservoirs, respectively, in Kelvin. The temperature at which ice and water coexist (melting point of ice) at 1.0 atm is 0°C or 273.15 K, and the temperature at which water and steam coexist (boiling point of water) at 1.0 atm is 100°C or 373.15 K. Thus, $\eta = 1 - \frac{273.15}{373.15} ≈ 0.27$ or 27%.

Quiz 11: Using Energy

A reversible engine takes in heat at a rate of 555 W and exhausts heat at 482 W. (a)How much power does it produce? (b)What is its efficiency? (c)If operated in reverse as a refrigerator, what would be its performance coefficient (COP)?

An ideal Carnot engine operates between a warm reservoir at 233 K and a colder reservoir. During each cycle, this engine extracts $15.0 \mathrm {~J}$ of heat from the warm reservoir and does $4.0 \mathrm {~J}$ of work. What is the temperature of the colder reservoir?

Suppose that the Department of Energy develops a new reversible engine that has a coefficient of performance (COP) of 4.0 when operated as a refrigerator and a COP of 5.0 when operated as a heat pump. What is its thermal efficiency when operated as a heat engine doing work?

If the efficiency of a reversible engine is 28%, what is its COP (performance coefficient)operated (a)as a refrigerator, and (b)as a heat pump?

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

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 $40.0 \%$ What is the temperature of the warm reservoir?

An ideal reversible heat pump is taking heat from the outside air at -10.0°C and discharging it into the house at 18.0°C. What is the coefficient of performance of this heat pump?

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?

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 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 Carnot engine operates between two reservoirs with unknown temperatures. If the Carnot engine operates at $67 \%$ efficiency, what is the ratio of the absolute temperatures of the reservoirs, T_c/T_h?

The "hot shot" heat engine operating between 40°C and 380°C has an efficiency that is 60% of that of an ideal Carnot engine operating between the same temperatures. If the "hot shot" engine absorbs heat at a rate of 60 kW, at what rate does it exhaust heat?

During each cycle of operation, a refrigerator absorbs 230 J of heat from the freezer and expels 356 J of heat to the room. How much work input is required in each cycle?

A refrigerator has a performance coefficient (COP)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?

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 refrigerator has a coefficient of performance equal to 4.2. How much work must be done on the operating gas in the refrigerator in order to remove 250 J of heat from the interior compartment?

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.

During each cycle, the compressor in a certain ideal Carnot refrigerator performs 480 J of work to remove 150 J of heat from the interior of the refrigerator. How much heat do the coils behind the refrigerator discharge into the kitchen each cycle?

What is the efficiency of an ideal Carnot 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 atm for both reservoirs.

Quiz 11: Using Energy

A reversible engine takes in heat at a rate of 555 W and exhausts heat at 482 W. (a)How much power does it produce? (b)What is its efficiency? (c)If operated in reverse as a refrigerator, what would be its performance coefficient (COP)?

An ideal Carnot engine operates between a warm reservoir at 233 K and a colder reservoir. During each cycle, this engine extracts 15.0 J15.0 \mathrm {~J}15.0 J of heat from the warm reservoir and does 4.0 J4.0 \mathrm {~J}4.0 J of work. What is the temperature of the colder reservoir?

Suppose that the Department of Energy develops a new reversible engine that has a coefficient of performance (COP) of 4.0 when operated as a refrigerator and a COP of 5.0 when operated as a heat pump. What is its thermal efficiency when operated as a heat engine doing work?

If the efficiency of a reversible engine is 28%, what is its COP (performance coefficient)operated (a)as a refrigerator, and (b)as a heat pump?

An ideal Carnot engine operates between a high temperature reservoir at 492 K492 \mathrm {~K}492 K and a river with water at 290 K.290 \mathrm {~K} .290 K. If it absorbs 4000 J4000 \mathrm {~J}4000 J of heat each cycle, how much work per cycle does it perform?

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

An ideal Carnot engine operating between a warm reservoir of unknown temperature and a cold reservoir at 1.76 K1.76 \mathrm {~K}1.76 K has an efficiency of 40.0%40.0 \%40.0% What is the temperature of the warm reservoir?

An ideal reversible heat pump is taking heat from the outside air at -10.0°C and discharging it into the house at 18.0°C. What is the coefficient of performance of this heat pump?

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?

An ideal Carnot engine operating between a warm reservoir of unknown temperature and a cold reservoir at 1.76 K1.76 \mathrm {~K}1.76 K has an efficiency of 11.0%11.0 \%11.0% What is the temperature of the warm reservoir?

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 Carnot engine operates between two reservoirs with unknown temperatures. If the Carnot engine operates at 67%67 \%67% efficiency, what is the ratio of the absolute temperatures of the reservoirs, Tc/Th?

The "hot shot" heat engine operating between 40°C and 380°C has an efficiency that is 60% of that of an ideal Carnot engine operating between the same temperatures. If the "hot shot" engine absorbs heat at a rate of 60 kW, at what rate does it exhaust heat?

During each cycle of operation, a refrigerator absorbs 230 J of heat from the freezer and expels 356 J of heat to the room. How much work input is required in each cycle?

A refrigerator has a performance coefficient (COP)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?

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 refrigerator has a coefficient of performance equal to 4.2. How much work must be done on the operating gas in the refrigerator in order to remove 250 J of heat from the interior compartment?

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.

During each cycle, the compressor in a certain ideal Carnot refrigerator performs 480 J of work to remove 150 J of heat from the interior of the refrigerator. How much heat do the coils behind the refrigerator discharge into the kitchen each cycle?

What is the efficiency of an ideal Carnot 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 atm for both reservoirs.

An ideal Carnot engine operates between a warm reservoir at 233 K and a colder reservoir. During each cycle, this engine extracts $15.0 \mathrm {~J}$ of heat from the warm reservoir and does $4.0 \mathrm {~J}$ of work. What is the temperature of the colder reservoir?

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 ideal Carnot engine operating between a warm reservoir of unknown temperature and a cold reservoir at $1.76 \mathrm {~K}$ has an efficiency of $40.0 \%$ What is the temperature of the warm reservoir?

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 Carnot engine operates between two reservoirs with unknown temperatures. If the Carnot engine operates at $67 \%$ efficiency, what is the ratio of the absolute temperatures of the reservoirs, T_c/T_h?