Question 1

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 2

A closed 2.0-L container holds 3.0 mol of an ideal gas.If 150 J of heat is added,what is the change in internal energy of the system?

Accepted Answer

According to the first law of thermodynamics, the change in internal energy of a system is equal to the heat added to the system minus the work done by the system: 
ΔU = Q - W 
Since the container is closed, no work is done by the gas (i.e. there is no change in volume), so W=0. Therefore, ΔU = Q. Plugging in the given values, we have:
ΔU = 150 J 
Therefore, the change in internal energy is equal to the heat added, which is 150 J. The correct answer is (C).

Question 3

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 efficiency of a heat engine is calculated using the formula: Efficiency = (Work output / Heat input) * 100%. The work output is the heat input minus the heat lost, which is 6000 J - 3600 J = 2400 J. Therefore, the efficiency is (2400 J / 6000 J) * 100% = 40%.

Question 4

In an isobaric process 3.6 × 10⁴ J of work is done on a quantity of gas while its volume changes from 2.3 m³ to 1.1 m³.What is the pressure during this process?

Accepted Answer

In an isobaric process, the pressure remains constant. Therefore, from the work done equation:
work = pressure x change in volume
we can solve for the pressure:
pressure = work / change in volume
Substituting the given values:
pressure = 3.6 × 10^14 J / ((1.1 - 2.3) m^3)
pressure = -3.6 × 10^14 J / (1.2 m^3)   (Note: negative sign indicates work is done on the gas)
pressure = 3.0 × 10^14 Pa

Question 5

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 answer of A cylinder containing an ideal gas has...

Question 6

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

During step 3, the system does work on the surroundings and energy is transferred into the system in the form of heat, causing an increase in internal energy. During step 4, the system undergoes adiabatic compression, resulting in an increase in temperature and thus an increase in internal energy. Therefore, the internal energy increases during steps 3 and 4.

Question 7

An electrical generating plant operates at a boiler temperature of 220°C and exhausts the unused heat into a nearby river at 19°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°C = 273 K)

Accepted Answer

The theoretical efficiency is calculated using the Carnot efficiency formula: 1 - (T_cold/T_hot). The actual efficiency is 3/5 of this value. Using the actual efficiency and the power output, we can find the heat input required.

Question 8

A 4-mol ideal gas system undergoes an adiabatic process where it expands and does 28 J of work on its environment.What is its change in internal energy?

Accepted Answer

In an adiabatic process, the change in internal energy is equal to the work done on or by the system. Since the gas does 28 J of work on the environment, the internal energy decreases by 28 J.

Question 9

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 answer of Three Carnot engines operate between temperature reservoirs...

Question 10

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

Accepted Answer

The maximum theoretical efficiency of the plant can be calculated using the formula: efficiency = 1 - Tcold/Thot, where Tcold is the temperature of the cold reservoir (in Kelvin) and Thot is the temperature of the hot reservoir (in Kelvin). Converting the given temperatures to Kelvin, we get:
Tcold = 20 + 273 = 293 K
Thot = 200 + 273 = 473 K
Using the formula, efficiency = 1 - 293/473 = 0.38, which is 38%. Therefore, the correct choice is B.

Question 11

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 operating between two reservoirs is given by the Carnot efficiency, which is equal to (Th - Tc)/Th, where Th and Tc are the temperatures of the hot and cold reservoirs, respectively. Therefore, the maximum efficiency of this engine is (500-300)/500 = 40%. The correct choice is C.

Question 12

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 13

A 2.0-mol ideal gas system is maintained at a constant volume of 4.0 L.If 200 J of heat is added,what is the work done on the system?

Accepted Answer

Since the system is maintained at constant volume, the work done is zero (W=0). Therefore, the answer is A.

Question 14

Which of the processes on a monatomic ideal gas given below will result in the temperature of the gas increasing? W is the work done by the gas.

Accepted Answer

The change in internal energy of a monatomic ideal gas is given by ΔU = 3/2nRΔT, where n is the number of moles, R is the gas constant, and ΔT is the change in temperature. According to the first law of thermodynamics, ΔU = Q - W, where Q is the heat transferred to the gas and W is the work done by the gas. Therefore, ΔT = (2/3)(Q - W)/nR. In order for the temperature to increase, ΔT must be positive. This occurs when Q > W, or when Q = 2W. Therefore, the correct answer is choice C.

Question 15

The volume of an ideal gas changes from 0.40 to 0.55 m³ although its pressure remains constant at 50,000 Pa.What work is done by the system ON its environment?

Accepted Answer

The work done by the system (gas) on the environment is given by the formula: 
W = PΔV, where P is the constant pressure and ΔV is the change in volume.

Here, P = 50,000 Pa and ΔV = (0.55 - 0.40)m³ = 0.15 m³

Therefore, W = (50,000 Pa) x (0.15 m³) = 7500 J

Hence, the correct answer is (C) 7500 J.

Question 16

A system is acted on by its surroundings in such a way that it receives 50 J of heat while simultaneously doing 70 J of work.What is its net change in internal energy?

Accepted Answer

According to the first law of thermodynamics, the change in internal energy (ΔU) of a system is equal to the heat (Q) added to the system minus the work (W) done by the system: ΔU = Q - W. In this case, ΔU = 50 J - 70 J = -20 J. The negative sign indicates that the internal energy of the system has decreased. Therefore, the best choice is B.

Question 17

A 4-mol ideal gas system undergoes an adiabatic process where it expands and does 28 J of work on its environment.How much heat is received by the system?

Accepted Answer

In an adiabatic process, there is no heat exchange between the system and its environment. Therefore, the heat received by the system is zero (Q = 0). The only work is done by the system, which is given as 28 J.

Question 18

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 19

A system has an increase in internal energy of 60 J while 90 J was removed from the system by heat.How much work was involved during this process and was it done on the system or done on its environment?

Accepted Answer

According to the first law of thermodynamics, energy can neither be created nor destroyed, only transferred between systems. Therefore, the total change in energy of the system is equal to the amount of heat added or removed from the system plus the amount of work done on or by the system. In this case, the internal energy of the system increased by 60 J while 90 J was removed from the system by heat. Therefore, the total change in energy of the system is -30 J. This means that 30 J of work was done on the system (since the sign of work done on the system is opposite to that of the change in energy of the system). Therefore, the correct choice is C, 150 J on the system.

Question 20

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 overall efficiency is the product of the efficiencies of each stage: 0.88 * 0.30 = 0.264, which is 26.4%, less than 30%.

Quiz 16: Electrical Energy and Capacitance: Part A