Question 1

Three Carnot engines operate between temperature reservoirs as follows: Engine A: T_h = 1300 K, T_c = 1000 K; Engine B: T_h = 1000 K, T_c = 700 K; Engine C: T_h = 500 K, T_c = 350 K. Which two engines have the same thermal efficiency?

Accepted Answer

The thermal efficiency of a Carnot engine solely depends on the temperature difference between the hot and cold reservoirs. Therefore, engines A and B cannot have the same thermal efficiency since their temperature differences are different. However, engines B and C both have a temperature difference of 300 K, so they must have the same thermal efficiency.

Question 2

An electrical generating plant operates at a boiler temperature of 200$\degree$C and exhausts the unused heat into a nearby river at 20$\degree$C. What is the maximum theoretical efficiency of the plant? (0$\degree$C = 273 K)

Accepted Answer

The maximum theoretical efficiency of a heat engine is given by the Carnot efficiency: 1 - (Tc/Th), where Tc is the cold reservoir temperature and Th is the hot reservoir temperature, both in Kelvin. Converting the given temperatures to Kelvin: Th = 200 + 273 = 473 K, Tc = 20 + 273 = 293 K. The efficiency is 1 - (293/473) = 0.380, or 38%.

Question 3

Consider a Carnot cycle starting at the state of highest pressure and smallest volume. Call the isothermal expansion from this state step 1, the adiabatic expansion which follows step 2, the isothermal compression that then follows step 3, and the adiabatic compression which returns the system to the initial state step 4. In which steps does the internal energy of the system increase?

Accepted Answer

In the adiabatic expansion (step 2), the internal energy of the system increases due to the work done by the system on its surroundings without any heat transfer. In the isothermal compression (step 3), the internal energy of the system also increases due to the heat transfer from the surroundings to the system. Therefore, the internal energy of the system increases in steps 2 and 3.

Question 4

The maximum theoretical thermodynamic efficiency of a heat engine operating between hot and cold reservoirs is a function of which of the following?

Accepted Answer

The maximum theoretical thermodynamic efficiency of a heat engine is given by the Carnot efficiency which depends on both the hot and cold reservoir temperatures. Therefore, the correct choice is C - both hot and cold reservoir temperatures.

Question 5

An electrical generating plant operates at a boiler temperature of 220$\degree$C and exhausts the unused heat into a nearby river at 19$\degree$C. If the generating plant has a power output of 800 megawatts (MW) and if the actual efficiency is 3/5 the theoretical efficiency, how much heat per second must be delivered to the boiler? (0$\degree$C = 273 K)

Accepted Answer

The theoretical efficiency (Carnot efficiency) is calculated using the temperatures in Kelvin: η = 1 - (T_cold/T_hot). Convert the temperatures: T_hot = 220 + 273 = 493 K, T_cold = 19 + 273 = 292 K. η = 1 - (292/493) = 0.407. The actual efficiency is 3/5 of this: 0.407 * 3/5 = 0.2442. The power output is 800 MW, so the heat input Q_in = Power output / Efficiency = 800 MW / 0.2442 ≈ 3270 MW.

Question 6

A heat engine operating between a pair of hot and cold reservoirs with respective temperatures of 500 K and 300 K will have what maximum efficiency?

Accepted Answer

The maximum efficiency of a heat engine is given by the Carnot efficiency, which is:
Efficiency = 1 - (Tc/Th)
where Tc is the temperature of the cold reservoir and Th is the temperature of the hot reservoir. Substituting the values, we get:
Efficiency = 1 - (300/500) = 0.4 or 40%
Therefore, the maximum efficiency of the heat engine is 40%.

Question 7

A heat engine receives 6000 J of heat from its combustion process and loses 3600 J through the exhaust and friction. What is its efficiency?

Accepted Answer

The answer of A heat engine receives 6000 J of...

Question 8

A turbine takes in 1000 K steam and exhausts the steam at a temperature of 400 K. What is the maximum theoretical efficiency of this system?

Accepted Answer

The answer of A turbine takes in 1000 K steam...

Question 9

According to the second law of thermodynamics, which of the following applies to the heat received from a high temperature reservoir by a heat engine operating in a complete cycle?

Accepted Answer

The second law of thermodynamics states that it is impossible to convert all of the heat received from a high temperature reservoir into work. Some of the heat must be rejected to a low temperature reservoir, resulting in a decrease in the amount of available energy to do work. Therefore, option D is the correct choice.

Question 10

A thermodynamic process that happens very quickly tends to be:

Accepted Answer

A thermodynamic process that happens very quickly tends to be adiabatic because there is no time for heat to transfer between the system and its surroundings. Adiabatic processes involve a change in internal energy without a change in heat transfer. The other options (isobaric, isothermal, and isovolumetric) imply a slower process with more time for heat transfer to occur.

Question 11

An electrical power plant manages to send 88% of the heat produced in the burning of fossil fuel into the water-to-steam conversion. Of the heat carried by the steam, 30% is converted to the mechanical energy of the spinning turbine. Which of the following choices best describes the overall efficiency of the heat-to-work conversion in the plant (as a percentage)?

Accepted Answer

The answer of An electrical power plant manages to send...

Question 12

In an isochoric process where the pressure increases from  to  , does the internal energy of the system increase or decrease and does the temperature increase or decrease?

Accepted Answer

The answer of In an isochoric process where the pressure...

Question 13

A heat engine exhausts 4000 J of heat while performing 2000 J of useful work. What is the efficiency of the engine?

Accepted Answer

The efficiency of the engine is given by (useful work output/heat input) x 100%. Therefore, the efficiency is (2000/4000) x 100% = 50%. Option B is the closest choice, which is 33%. Therefore, the correct answer is B.

Question 14

A cylinder containing an ideal gas has a volume of 3.0 m³ and a pressure of 1.0 *10⁵ Pa at a temperature of 300 K. The cylinder is placed against a metal block that is maintained at 900 K, and the gas expands as the pressure remains constant until the temperature of the gas reaches 900 K. The change in internal energy of the gas is +6.0 *10⁵ J. How much heat did the gas absorb?

Accepted Answer

The heat absorbed by the gas can be calculated using the first law of thermodynamics: ΔU = Q - W. Given ΔU = +6.0 x 10^5 J and the work done by the gas (W) is PΔV = 1.0 x 10^5 Pa x (9 m^3 - 3 m^3) = 6.0 x 10^5 J, we find Q = ΔU + W = 6.0 x 10^5 J + 6.0 x 10^5 J = 12 x 10^5 J.

Question 15

A 5-mol ideal gas system undergoes an adiabatic free expansion (a rapid expansion into a vacuum), going from an initial volume of 10 L to a final volume of 20 L. How much work is done on the system during this adiabatic free expansion?

Accepted Answer

In an adiabatic free expansion, the gas expands into a vacuum without any external pressure, so no work is done on or by the system.

Question 16

During each cycle of operation a refrigerator absorbs 45 cal from the freezer compartment and expels 85 cal to the room. If one cycle occurs every 8.0 s, how many minutes will it take to freeze 500 g of water, initially at 0$\degree$C? (L_v = 80 cal/g)

Accepted Answer

The refrigerator removes 45 cal from the freezer compartment every 8.0 s, so it removes 45 cal / 8.0 s = 5.6 cal/s. To freeze 500 g of water, we need to remove 500 g * 80 cal/g = 40,000 cal. So, it will take 40,000 cal / 5.6 cal/s = 7143 s = 120 min.

Question 17

Which of the following increases the internal energy of a solid metal rod?

Accepted Answer

Having the rod absorb heat increases its internal energy by increasing the kinetic energy of its particles. Option A raises the potential energy of the rod, but does not increase internal energy. Option B only changes the rod's external motion and has no effect on internal energy. Option C transfers energy into the metal rod, but does not necessarily increase its internal energy unless the heat causes a temperature increase.

Question 18

If a heat engine has an efficiency of 30% and its power output is 600 W, what is the rate of heat input from the combustion phase?

Accepted Answer

The efficiency of a heat engine is defined as the ratio of the work output (in this case, 600 W) to the heat input. Therefore, we can write:
efficiency = work output / heat input
0.30 = 600 W / heat input
Solving for the heat input, we get:
heat input = 600 W / 0.30 = 2 000 W
So the rate of heat input from the combustion phase is 2 000 W. Therefore the correct answer is choice letter C.

Question 19

A quantity of monatomic ideal gas expands adiabatically from a volume of 2.0 liters to 4.0 liters. If the initial pressure is P₀, what is the final pressure?

Accepted Answer

The answer of A quantity of monatomic ideal gas expands...

Question 20

Heat is applied to an ice-water mixture to melt some of the ice. In this process:

Accepted Answer

The melting of ice occurs at a constant temperature until all of the ice has melted. Therefore, the temperature does not increase until all of the ice has melted. Since the heat is causing a phase change, no work is being done. However, the internal energy of the system is increasing as the ice melts, so Option C is correct.  Option D is incorrect as Option A is not correct.

Quiz 16: Thermodynamics

Three Carnot engines operate between temperature reservoirs as follows: Engine A: T_h = 1300 K, T_c = 1000 K; Engine B: T_h = 1000 K, T_c = 700 K; Engine C: T_h = 500 K, T_c = 350 K. Which two engines have the same thermal efficiency?

An electrical generating plant operates at a boiler temperature of 200 $\degree$ C and exhausts the unused heat into a nearby river at 20 $\degree$ C. What is the maximum theoretical efficiency of the plant? (0 $\degree$ C = 273 K)

The maximum theoretical thermodynamic efficiency of a heat engine operating between hot and cold reservoirs is a function of which of the following?

A heat engine operating between a pair of hot and cold reservoirs with respective temperatures of 500 K and 300 K will have what maximum efficiency?

A heat engine receives 6000 J of heat from its combustion process and loses 3600 J through the exhaust and friction. What is its efficiency?

A turbine takes in 1000 K steam and exhausts the steam at a temperature of 400 K. What is the maximum theoretical efficiency of this system?

According to the second law of thermodynamics, which of the following applies to the heat received from a high temperature reservoir by a heat engine operating in a complete cycle?

A thermodynamic process that happens very quickly tends to be:

In an isochoric process where the pressure increases from to , does the internal energy of the system increase or decrease and does the temperature increase or decrease?

A heat engine exhausts 4000 J of heat while performing 2000 J of useful work. What is the efficiency of the engine?

A 5-mol ideal gas system undergoes an adiabatic free expansion (a rapid expansion into a vacuum) , going from an initial volume of 10 L to a final volume of 20 L. How much work is done on the system during this adiabatic free expansion?

During each cycle of operation a refrigerator absorbs 45 cal from the freezer compartment and expels 85 cal to the room. If one cycle occurs every 8.0 s, how many minutes will it take to freeze 500 g of water, initially at 0 $\degree$ C? (L_v = 80 cal/g)

Which of the following increases the internal energy of a solid metal rod?

If a heat engine has an efficiency of 30% and its power output is 600 W, what is the rate of heat input from the combustion phase?

A quantity of monatomic ideal gas expands adiabatically from a volume of 2.0 liters to 4.0 liters. If the initial pressure is P₀, what is the final pressure?

Heat is applied to an ice-water mixture to melt some of the ice. In this process:

Quiz 16: Thermodynamics

Three Carnot engines operate between temperature reservoirs as follows: Engine A: Th = 1300 K, Tc = 1000 K; Engine B: Th = 1000 K, Tc = 700 K; Engine C: Th = 500 K, Tc = 350 K. Which two engines have the same thermal efficiency?

An electrical generating plant operates at a boiler temperature of 200 °\degree° C and exhausts the unused heat into a nearby river at 20 °\degree° C. What is the maximum theoretical efficiency of the plant? (0 °\degree° C = 273 K)

The maximum theoretical thermodynamic efficiency of a heat engine operating between hot and cold reservoirs is a function of which of the following?

A heat engine operating between a pair of hot and cold reservoirs with respective temperatures of 500 K and 300 K will have what maximum efficiency?

A heat engine receives 6000 J of heat from its combustion process and loses 3600 J through the exhaust and friction. What is its efficiency?

A turbine takes in 1000 K steam and exhausts the steam at a temperature of 400 K. What is the maximum theoretical efficiency of this system?

According to the second law of thermodynamics, which of the following applies to the heat received from a high temperature reservoir by a heat engine operating in a complete cycle?

A thermodynamic process that happens very quickly tends to be:

In an isochoric process where the pressure increases from to , does the internal energy of the system increase or decrease and does the temperature increase or decrease?

A heat engine exhausts 4000 J of heat while performing 2000 J of useful work. What is the efficiency of the engine?

A 5-mol ideal gas system undergoes an adiabatic free expansion (a rapid expansion into a vacuum) , going from an initial volume of 10 L to a final volume of 20 L. How much work is done on the system during this adiabatic free expansion?

During each cycle of operation a refrigerator absorbs 45 cal from the freezer compartment and expels 85 cal to the room. If one cycle occurs every 8.0 s, how many minutes will it take to freeze 500 g of water, initially at 0 °\degree° C? (Lv = 80 cal/g)

Which of the following increases the internal energy of a solid metal rod?

If a heat engine has an efficiency of 30% and its power output is 600 W, what is the rate of heat input from the combustion phase?

A quantity of monatomic ideal gas expands adiabatically from a volume of 2.0 liters to 4.0 liters. If the initial pressure is P0, what is the final pressure?

Heat is applied to an ice-water mixture to melt some of the ice. In this process:

Three Carnot engines operate between temperature reservoirs as follows: Engine A: T_h = 1300 K, T_c = 1000 K; Engine B: T_h = 1000 K, T_c = 700 K; Engine C: T_h = 500 K, T_c = 350 K. Which two engines have the same thermal efficiency?

An electrical generating plant operates at a boiler temperature of 200 $\degree$ C and exhausts the unused heat into a nearby river at 20 $\degree$ C. What is the maximum theoretical efficiency of the plant? (0 $\degree$ C = 273 K)

During each cycle of operation a refrigerator absorbs 45 cal from the freezer compartment and expels 85 cal to the room. If one cycle occurs every 8.0 s, how many minutes will it take to freeze 500 g of water, initially at 0 $\degree$ C? (L_v = 80 cal/g)

A quantity of monatomic ideal gas expands adiabatically from a volume of 2.0 liters to 4.0 liters. If the initial pressure is P₀, what is the final pressure?