PHYS Ch 11 Quiz – Thermodynamics and Heat Engines Study Guide

Q1. A system receives 100 J of heat. If the thermal energy of the system remains constant, how much work does the system do?

Background

Topic: First Law of Thermodynamics

This question tests your understanding of energy conservation in thermodynamic systems, specifically the relationship between heat, work, and internal energy.

Key Terms and Formulas:

• First Law of Thermodynamics: $\Delta E = Q - W$

• $\Delta E$ = change in internal energy

• $Q$ = heat added to the system

• $W$ = work done by the system

Step-by-Step Guidance

1. Identify what is given: $Q = 100\ \mathrm{J}$, $\Delta E = 0$ (thermal energy remains constant).

2. Substitute the known values into the First Law: $0 = 100 - W$.

3. Rearrange the equation to solve for $W$.

Try solving on your own before revealing the answer!

Q2. Engine 1 takes in 100 J of heat from a hot reservoir and does 20 J of work. Engine 2 takes in the same amount of heat and does 25 J of work. Is the efficiency of engine 1 greater than, less than, or equal to the efficiency of engine 2?

Background

Topic: Heat Engine Efficiency

This question tests your ability to compare the efficiencies of two heat engines based on the work output and heat input.

Key Terms and Formulas:

• Efficiency of a heat engine: $e = \frac{W}{Q}$

• $W$ = work done by the engine

• $Q$ = heat absorbed from the hot reservoir

Step-by-Step Guidance

1. Calculate the efficiency for Engine 1: $e_1 = \frac{20}{100}$.

2. Calculate the efficiency for Engine 2: $e_2 = \frac{25}{100}$.

3. Compare $e_1$ and $e_2$ to determine which is greater.

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Q3. Engine 1 takes in 100 J of heat and does 20 J of work. Engine 2 takes in 600 J of heat and does 60 J of work. Is the efficiency of engine 1 greater than, less than, or equal to the efficiency of engine 2?

Background

Topic: Heat Engine Efficiency Comparison

This question asks you to compare the efficiencies of two engines with different heat inputs and work outputs.

Key Terms and Formulas:

• Efficiency: $e = \frac{W}{Q}$

Step-by-Step Guidance

1. Calculate $e_1 = \frac{20}{100}$ for Engine 1.

2. Calculate $e_2 = \frac{60}{600}$ for Engine 2.

3. Compare the two efficiencies to answer the question.

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Q4. Which of the following equations illustrates the First Law of Thermodynamics?

Background

Topic: First Law of Thermodynamics

This question tests your ability to recognize the correct mathematical statement of the First Law of Thermodynamics.

Key Terms and Formulas:

• First Law: $\Delta E = Q - W$

Step-by-Step Guidance

1. Review each option and recall the standard form of the First Law.

2. Identify which equation matches $\Delta E = Q - W$.

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Q5. In an adiabatic compression of an ideal gas, no heat is exchanged with the surroundings ($Q = 0$). What happens to the temperature of the gas?

Background

Topic: Adiabatic Processes

This question tests your understanding of how temperature changes during adiabatic compression, where no heat is transferred.

Key Terms and Formulas:

• Adiabatic process: $Q = 0$

• First Law: $\Delta E = Q - W$

• For compression, work is done on the gas ($W < 0$)

Step-by-Step Guidance

1. Recall that $Q = 0$ in an adiabatic process.

2. Consider the sign of work during compression (work done on the gas).

3. Use the First Law to determine the effect on internal energy and temperature.

Try solving on your own before revealing the answer!

Q6. Find the heat associated with this process: $W = 50\ \mathrm{J}$, $\Delta E = 50\ \mathrm{J}$

Background

Topic: First Law of Thermodynamics (Solving for Heat)

This question asks you to solve for the heat transferred in a process, given the work done and the change in internal energy.

Key Terms and Formulas:

• First Law: $\Delta E = Q - W$

Step-by-Step Guidance

1. Substitute the given values into the First Law: $50 = Q - 50$.

2. Rearrange the equation to solve for $Q$.

Try solving on your own before revealing the answer!

Q7. A runner does $8.2 \times 10^6$ J of work and gives off $3.3 \times 10^6$ J of heat. Determine $\Delta E$ for the runner.

Background

Topic: First Law of Thermodynamics (Application to Biological Systems)

This question tests your ability to apply the First Law to a real-world scenario involving work and heat loss.

Key Terms and Formulas:

• First Law: $\Delta E = Q - W$

• Here, $Q$ is heat given off (so it is negative)

Step-by-Step Guidance

1. Assign the correct signs: $Q = -3.3 \times 10^6$ J (heat lost), $W = 8.2 \times 10^6$ J (work done by the runner).

2. Substitute into the First Law: $\Delta E = (-3.3 \times 10^6) - (8.2 \times 10^6)$.

3. Simplify the expression to find $\Delta E$.

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Q8. Which of the following physical quantities is zero in a constant-volume process?

Background

Topic: Thermodynamic Processes

This question tests your understanding of what happens during a constant-volume (isochoric) process.

Key Terms and Formulas:

• Work done: $W = P \Delta V$

• Constant volume: $\Delta V = 0$

Step-by-Step Guidance

1. Recall that in a constant-volume process, $\Delta V = 0$.

2. Substitute into the work formula to determine which quantity is zero.

Try solving on your own before revealing the answer!

Q9. Which of the following physical quantities is zero in an isothermal process?

Background

Topic: Isothermal Processes

This question tests your understanding of what remains constant or becomes zero during an isothermal process.

Key Terms and Formulas:

• Isothermal: $\Delta T = 0$

• For an ideal gas, $\Delta E = n C_v \Delta T$

Step-by-Step Guidance

1. Recall that temperature does not change in an isothermal process.

2. Use the internal energy formula to determine which quantity is zero.

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Q10. Which of the following physical quantities is zero in an adiabatic process?

Background

Topic: Adiabatic Processes

This question tests your understanding of what is zero during an adiabatic process.

Key Terms and Formulas:

• Adiabatic: $Q = 0$

Step-by-Step Guidance

1. Recall the definition of an adiabatic process.

2. Identify which physical quantity is zero based on the definition.

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Q11. Use the graph to determine work done in this process.

Background

Topic: Work Done by a Gas in a PV Diagram

This question tests your ability to interpret a PV diagram and calculate the net work done in a thermodynamic cycle.

Key Terms and Formulas:

• Work done in a PV diagram: Area enclosed by the cycle

• For a rectangle: $W = (P_{high} - P_{low}) \times (V_{high} - V_{low})$

Step-by-Step Guidance

1. Identify the coordinates of the rectangle (pressures and volumes at each corner).

2. Calculate the area enclosed by the cycle, which represents the net work done.

3. Multiply the difference in pressure by the difference in volume to find the area.

Try solving on your own before revealing the answer!

Q12. A process that occurs at a constant temperature is called:

Background

Topic: Thermodynamic Processes

This question tests your knowledge of terminology for thermodynamic processes.

Key Terms and Formulas:

• Isothermal: Constant temperature

• Adiabatic: No heat exchange

Step-by-Step Guidance

1. Recall the definitions of isothermal and adiabatic processes.

2. Match the correct term to the description.

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Q13. A fluid expands by $0.42\ \mathrm{m}^3$ at a pressure of $121\ \mathrm{kPa}$. How much work is done by the fluid?

Background

Topic: Work Done by Expanding Gas

This question tests your ability to calculate work done during an isobaric (constant pressure) expansion.

Key Terms and Formulas:

• Work: $W = P \Delta V$

• Pressure must be in Pascals (1 kPa = 1000 Pa)

Step-by-Step Guidance

1. Convert pressure to Pascals: $121\ \mathrm{kPa} = 121,000\ \mathrm{Pa}$.

2. Multiply pressure by the change in volume: $W = 121,000 \times 0.42$.

Try solving on your own before revealing the answer!

Q14. A gas is contained in a cylinder with a pressure of $140\ \mathrm{kPa}$ and an initial volume of $0.66\ \mathrm{m}^3$. How much work is done by the gas if it expands at constant pressure to twice the initial volume?

Background

Topic: Work Done by a Gas at Constant Pressure

This question tests your ability to calculate work done during an isobaric expansion when the volume changes.

Key Terms and Formulas:

• Work: $W = P \Delta V$

• Final volume: $V_f = 2 \times 0.66 = 1.32\ \mathrm{m}^3$

• Change in volume: $\Delta V = V_f - V_i$

Step-by-Step Guidance

1. Calculate the final volume: $V_f = 2 \times 0.66$.

2. Find the change in volume: $\Delta V = V_f - V_i$.

3. Convert pressure to Pascals: $140\ \mathrm{kPa} = 140,000\ \mathrm{Pa}$.

4. Multiply pressure by $\Delta V$ to find the work done.

Try solving on your own before revealing the answer!

Q15. If you rub your hands together, the entropy of the universe changes. Choose the best explanation for this.

Background

Topic: Entropy and the Second Law of Thermodynamics

This question tests your understanding of how entropy changes when energy is dissipated as heat.

Key Terms and Formulas:

• Entropy: A measure of disorder or randomness

• Second Law: Entropy of the universe increases in spontaneous processes

Step-by-Step Guidance

1. Consider what happens to the energy when you rub your hands together (heat is produced).

2. Think about how this heat affects the entropy of your hands and the surrounding air.

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Q16. A heat engine operates between a hot reservoir at temperature $T_h$ and a cold reservoir at $T_c$. If both temperatures are doubled, what happens to the efficiency of the engine?

Background

Topic: Carnot Engine Efficiency

This question tests your understanding of how the efficiency of an ideal (Carnot) engine depends on the temperatures of the reservoirs.

Key Terms and Formulas:

• Carnot efficiency: $e = 1 - \frac{T_c}{T_h}$

Step-by-Step Guidance

1. Write the original efficiency formula: $e = 1 - \frac{T_c}{T_h}$.

2. Substitute $T_h' = 2T_h$ and $T_c' = 2T_c$ into the formula.

3. Simplify to see how the efficiency changes.

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Q17. What is the efficiency of an engine that takes in 610 J of heat and does 230 J of work?

Background

Topic: Heat Engine Efficiency Calculation

This question tests your ability to calculate the efficiency of a heat engine given the heat input and work output.

Key Terms and Formulas:

• Efficiency: $e = \frac{W}{Q}$

• Express efficiency as a percentage: $e \times 100\%$

Step-by-Step Guidance

1. Substitute the given values into the efficiency formula: $e = \frac{230}{610}$.

2. Multiply by 100 to convert to a percentage.

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Q18. An engine receives 780 J of heat from a hot reservoir and does 110 J of work. What is the heat given off to the cold reservoir?

Background

Topic: Conservation of Energy in Heat Engines

This question tests your understanding of energy flow in a heat engine.

Key Terms and Formulas:

• First Law for engines: $Q_{in} = W + Q_{out}$

• $Q_{out}$ = heat expelled to the cold reservoir

Step-by-Step Guidance

1. Write the energy balance: $Q_{in} = W + Q_{out}$.

2. Substitute the given values: $780 = 110 + Q_{out}$.

3. Rearrange to solve for $Q_{out}$.

Try solving on your own before revealing the answer!

Q19. Absolute zero cannot be reached. True or False?

Background

Topic: Third Law of Thermodynamics

This question tests your understanding of the third law, which states that absolute zero is unattainable.

Key Terms and Formulas:

• Absolute zero: $0\ \mathrm{K}$, the lowest possible temperature

• Third Law: It is impossible to reach absolute zero in a finite number of steps

Step-by-Step Guidance

1. Recall the statement of the third law of thermodynamics.

2. Decide whether the statement is true or false based on the law.

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Q20. No engine can be 100% efficient. True or False?

Background

Topic: Second Law of Thermodynamics

This question tests your understanding of the limitations imposed by the second law on the efficiency of heat engines.

Key Terms and Formulas:

• Second Law: No engine can convert all heat into work; some energy is always lost as waste heat

Step-by-Step Guidance

1. Recall the implications of the second law for heat engine efficiency.

2. Decide whether the statement is true or false based on the law.

Try solving on your own before revealing the answer!