Thermodynamics: 100 Practice Questions

Topic 1: First Law of Thermodynamics & Internal Energy

Q1.

During a process, the internal energy of a gas increases by 156 J while it absorbs 383 J of heat. Find the work done by the gas.

Q2.

A system absorbs 447 J of heat and does 59 J of work on its surroundings. What is the change in internal energy?

Q3.

During a process, the internal energy of a gas increases by 389 J while it absorbs 734 J of heat. Find the work done by the gas.

Q4.

During a process, the internal energy of a gas increases by 284 J while it absorbs 595 J of heat. Find the work done by the gas.

Q5.

A system absorbs 880 J of heat and does 272 J of work on its surroundings. What is the change in internal energy?

Q6.

During a process, the internal energy of a gas increases by 240 J while it absorbs 735 J of heat. Find the work done by the gas.

Q7.

A system absorbs 467 J of heat and does 110 J of work on its surroundings. What is the change in internal energy?

Q8.

During a process, the internal energy of a gas increases by 286 J while it absorbs 888 J of heat. Find the work done by the gas.

Q9.

During a process, the internal energy of a gas increases by 343 J while it absorbs 255 J of heat. Find the work done by the gas.

Q10.

A system absorbs 552 J of heat and does 219 J of work on its surroundings. What is the change in internal energy?

Topic 2: Specific Heats & Degrees of Freedom

Q11.

For a specific ideal gas, the molar heat capacity at constant volume is $C_v = 3 R$. Calculate its molar heat capacity at constant pressure $C_p$ and the ratio $\gamma$.

Q12.

Calculate the heat required to raise the temperature of 4 moles of a monoatomic ideal gas by 50 K at constant volume. (Take R = 8.31 J/mol K)

Q13.

For a specific ideal gas, the molar heat capacity at constant volume is $C_v = 3 R$. Calculate its molar heat capacity at constant pressure $C_p$ and the ratio $\gamma$.

Q14.

Calculate the heat required to raise the temperature of 3 moles of a monoatomic ideal gas by 44 K at constant volume. (Take R = 8.31 J/mol K)

Q15.

For a specific ideal gas, the molar heat capacity at constant volume is $C_v = 3 R$. Calculate its molar heat capacity at constant pressure $C_p$ and the ratio $\gamma$.

Q16.

Calculate the heat required to raise the temperature of 5 moles of a monoatomic ideal gas by 16 K at constant volume. (Take R = 8.31 J/mol K)

Q17.

For a specific ideal gas, the molar heat capacity at constant volume is $C_v = 1.5 R$. Calculate its molar heat capacity at constant pressure $C_p$ and the ratio $\gamma$.

Q18.

Calculate the heat required to raise the temperature of 5 moles of a monoatomic ideal gas by 22 K at constant volume. (Take R = 8.31 J/mol K)

Q19.

For a specific ideal gas, the molar heat capacity at constant volume is $C_v = 2.5 R$. Calculate its molar heat capacity at constant pressure $C_p$ and the ratio $\gamma$.

Q20.

Calculate the heat required to raise the temperature of 5 moles of a monoatomic ideal gas by 27 K at constant volume. (Take R = 8.31 J/mol K)

Topic 3: Isothermal Processes

Q21.

1 moles of an ideal gas expands isothermally at 314 K such that its volume becomes 2 times the initial volume. Find the work done. (Take $R = 8.31, \ln(2) \approx 0.69$)

Q22.

3 moles of an ideal gas expands isothermally at 307 K such that its volume becomes 3 times the initial volume. Find the work done. (Take $R = 8.31, \ln(3) \approx 1.1$)

Q23.

2 moles of an ideal gas expands isothermally at 358 K such that its volume becomes 2 times the initial volume. Find the work done. (Take $R = 8.31, \ln(2) \approx 0.69$)

Q24.

4 moles of an ideal gas expands isothermally at 473 K such that its volume becomes 2 times the initial volume. Find the work done. (Take $R = 8.31, \ln(2) \approx 0.69$)

Q25.

4 moles of an ideal gas expands isothermally at 426 K such that its volume becomes 2 times the initial volume. Find the work done. (Take $R = 8.31, \ln(2) \approx 0.69$)

Q26.

1 moles of an ideal gas expands isothermally at 452 K such that its volume becomes 3 times the initial volume. Find the work done. (Take $R = 8.31, \ln(3) \approx 1.1$)

Q27.

2 moles of an ideal gas expands isothermally at 311 K such that its volume becomes 3 times the initial volume. Find the work done. (Take $R = 8.31, \ln(3) \approx 1.1$)

Q28.

1 moles of an ideal gas expands isothermally at 402 K such that its volume becomes 4 times the initial volume. Find the work done. (Take $R = 8.31, \ln(4) \approx 1.39$)

Q29.

1 moles of an ideal gas expands isothermally at 457 K such that its volume becomes 2 times the initial volume. Find the work done. (Take $R = 8.31, \ln(2) \approx 0.69$)

Q30.

1 moles of an ideal gas expands isothermally at 470 K such that its volume becomes 2 times the initial volume. Find the work done. (Take $R = 8.31, \ln(2) \approx 0.69$)

Topic 4: Adiabatic Processes

Q31.

An ideal diatomic gas ($\gamma = 1.4$) of 1 moles expands adiabatically, and its temperature drops from 401 K to 297 K. Calculate the work done by the gas. (Take R = 8.31)

Q32.

An ideal diatomic gas ($\gamma = 1.4$) of 2 moles expands adiabatically, and its temperature drops from 496 K to 307 K. Calculate the work done by the gas. (Take R = 8.31)

Q33.

An ideal diatomic gas ($\gamma = 1.4$) of 1 moles expands adiabatically, and its temperature drops from 512 K to 279 K. Calculate the work done by the gas. (Take R = 8.31)

Q34.

An ideal diatomic gas ($\gamma = 1.4$) of 3 moles expands adiabatically, and its temperature drops from 503 K to 246 K. Calculate the work done by the gas. (Take R = 8.31)

Q35.

An ideal diatomic gas ($\gamma = 1.4$) of 2 moles expands adiabatically, and its temperature drops from 535 K to 336 K. Calculate the work done by the gas. (Take R = 8.31)

Q36.

An ideal diatomic gas ($\gamma = 1.4$) of 2 moles expands adiabatically, and its temperature drops from 514 K to 312 K. Calculate the work done by the gas. (Take R = 8.31)

Q37.

An ideal diatomic gas ($\gamma = 1.4$) of 3 moles expands adiabatically, and its temperature drops from 492 K to 309 K. Calculate the work done by the gas. (Take R = 8.31)

Q38.

An ideal diatomic gas ($\gamma = 1.4$) of 2 moles expands adiabatically, and its temperature drops from 411 K to 332 K. Calculate the work done by the gas. (Take R = 8.31)

Q39.

An ideal diatomic gas ($\gamma = 1.4$) of 1 moles expands adiabatically, and its temperature drops from 405 K to 331 K. Calculate the work done by the gas. (Take R = 8.31)

Q40.

An ideal diatomic gas ($\gamma = 1.4$) of 2 moles expands adiabatically, and its temperature drops from 436 K to 320 K. Calculate the work done by the gas. (Take R = 8.31)

Topic 5: Isobaric and Isochoric Processes

Q41.

A gas expands from 9 L to 17 L against a constant external pressure of 4 atm. Calculate the work done in Joules. (1 atm = 101.3 J/L)

Q42.

A gas expands from 6 L to 20 L against a constant external pressure of 1 atm. Calculate the work done in Joules. (1 atm = 101.3 J/L)

Q43.

A gas expands from 7 L to 20 L against a constant external pressure of 3 atm. Calculate the work done in Joules. (1 atm = 101.3 J/L)

Q44.

A gas expands from 9 L to 21 L against a constant external pressure of 1 atm. Calculate the work done in Joules. (1 atm = 101.3 J/L)

Q45.

A gas expands from 10 L to 22 L against a constant external pressure of 2 atm. Calculate the work done in Joules. (1 atm = 101.3 J/L)

Q46.

A gas expands from 6 L to 23 L against a constant external pressure of 3 atm. Calculate the work done in Joules. (1 atm = 101.3 J/L)

Q47.

A gas expands from 9 L to 15 L against a constant external pressure of 5 atm. Calculate the work done in Joules. (1 atm = 101.3 J/L)

Q48.

A gas expands from 7 L to 22 L against a constant external pressure of 4 atm. Calculate the work done in Joules. (1 atm = 101.3 J/L)

Q49.

A gas expands from 7 L to 16 L against a constant external pressure of 1 atm. Calculate the work done in Joules. (1 atm = 101.3 J/L)

Q50.

A gas expands from 10 L to 16 L against a constant external pressure of 1 atm. Calculate the work done in Joules. (1 atm = 101.3 J/L)

Topic 6: Work Calculation from P-V Diagrams

Q51.

In a cyclic process plotted on a P-V diagram, the cycle forms a rectangle. The volumes alternate between 3 m$^3$ and 12 m$^3$, and the pressures alternate between 3 atm and 9 atm. If the cycle is clockwise, find the net work done.

Q52.

In a cyclic process plotted on a P-V diagram, the cycle forms a rectangle. The volumes alternate between 5 m$^3$ and 20 m$^3$, and the pressures alternate between 3 atm and 9 atm. If the cycle is clockwise, find the net work done.

Q53.

In a cyclic process plotted on a P-V diagram, the cycle forms a rectangle. The volumes alternate between 2 m$^3$ and 10 m$^3$, and the pressures alternate between 2 atm and 8 atm. If the cycle is clockwise, find the net work done.

Q54.

Q55.

In a cyclic process plotted on a P-V diagram, the cycle forms a rectangle. The volumes alternate between 1 m$^3$ and 3 m$^3$, and the pressures alternate between 2 atm and 8 atm. If the cycle is clockwise, find the net work done.

Q56.

In a cyclic process plotted on a P-V diagram, the cycle forms a rectangle. The volumes alternate between 5 m$^3$ and 25 m$^3$, and the pressures alternate between 3 atm and 12 atm. If the cycle is clockwise, find the net work done.

Q57.

In a cyclic process plotted on a P-V diagram, the cycle forms a rectangle. The volumes alternate between 2 m$^3$ and 6 m$^3$, and the pressures alternate between 2 atm and 8 atm. If the cycle is clockwise, find the net work done.

Q58.

In a cyclic process plotted on a P-V diagram, the cycle forms a rectangle. The volumes alternate between 3 m$^3$ and 9 m$^3$, and the pressures alternate between 2 atm and 8 atm. If the cycle is clockwise, find the net work done.

Q59.

In a cyclic process plotted on a P-V diagram, the cycle forms a rectangle. The volumes alternate between 3 m$^3$ and 9 m$^3$, and the pressures alternate between 2 atm and 6 atm. If the cycle is clockwise, find the net work done.

Q60.

In a cyclic process plotted on a P-V diagram, the cycle forms a rectangle. The volumes alternate between 4 m$^3$ and 12 m$^3$, and the pressures alternate between 3 atm and 12 atm. If the cycle is clockwise, find the net work done.

Topic 7: Heat Engines

Q61.

A heat engine absorbs 1841 J of heat from a hot reservoir and produces 395 J of useful work. Calculate its efficiency and the heat rejected to the sink.

Q62.

A heat engine absorbs 1537 J of heat from a hot reservoir and produces 355 J of useful work. Calculate its efficiency and the heat rejected to the sink.

Q63.

A heat engine absorbs 1533 J of heat from a hot reservoir and produces 254 J of useful work. Calculate its efficiency and the heat rejected to the sink.

Q64.

A heat engine absorbs 1911 J of heat from a hot reservoir and produces 310 J of useful work. Calculate its efficiency and the heat rejected to the sink.

Q65.

A heat engine absorbs 1016 J of heat from a hot reservoir and produces 212 J of useful work. Calculate its efficiency and the heat rejected to the sink.

Q66.

A heat engine absorbs 691 J of heat from a hot reservoir and produces 180 J of useful work. Calculate its efficiency and the heat rejected to the sink.

Q67.

A heat engine absorbs 1766 J of heat from a hot reservoir and produces 208 J of useful work. Calculate its efficiency and the heat rejected to the sink.

Q68.

A heat engine absorbs 1563 J of heat from a hot reservoir and produces 153 J of useful work. Calculate its efficiency and the heat rejected to the sink.

Q69.

A heat engine absorbs 801 J of heat from a hot reservoir and produces 378 J of useful work. Calculate its efficiency and the heat rejected to the sink.

Q70.

A heat engine absorbs 1119 J of heat from a hot reservoir and produces 157 J of useful work. Calculate its efficiency and the heat rejected to the sink.

Topic 8: Refrigerators and Heat Pumps

Q71.

A refrigerator's compressor does 133 J of work per cycle to extract 574 J of heat from the cold interior. Calculate its Coefficient of Performance (COP) and the heat rejected to the room.

Q72.

A refrigerator's compressor does 123 J of work per cycle to extract 675 J of heat from the cold interior. Calculate its Coefficient of Performance (COP) and the heat rejected to the room.

Q73.

A refrigerator's compressor does 192 J of work per cycle to extract 345 J of heat from the cold interior. Calculate its Coefficient of Performance (COP) and the heat rejected to the room.

Q74.

A refrigerator's compressor does 61 J of work per cycle to extract 799 J of heat from the cold interior. Calculate its Coefficient of Performance (COP) and the heat rejected to the room.

Q75.

A refrigerator's compressor does 230 J of work per cycle to extract 272 J of heat from the cold interior. Calculate its Coefficient of Performance (COP) and the heat rejected to the room.

Q76.

A refrigerator's compressor does 88 J of work per cycle to extract 353 J of heat from the cold interior. Calculate its Coefficient of Performance (COP) and the heat rejected to the room.

Q77.

A refrigerator's compressor does 245 J of work per cycle to extract 445 J of heat from the cold interior. Calculate its Coefficient of Performance (COP) and the heat rejected to the room.

Q78.

A refrigerator's compressor does 75 J of work per cycle to extract 608 J of heat from the cold interior. Calculate its Coefficient of Performance (COP) and the heat rejected to the room.

Q79.

A refrigerator's compressor does 181 J of work per cycle to extract 638 J of heat from the cold interior. Calculate its Coefficient of Performance (COP) and the heat rejected to the room.

Q80.

A refrigerator's compressor does 111 J of work per cycle to extract 490 J of heat from the cold interior. Calculate its Coefficient of Performance (COP) and the heat rejected to the room.

Topic 9: Carnot Engine Efficiency

Q81.

A Carnot engine operates between a hot reservoir at 162$^\circ$C and a cold sink at 26$^\circ$C. Calculate its theoretical maximum efficiency.

Q82.

A Carnot engine operates between a hot reservoir at 194$^\circ$C and a cold sink at 28$^\circ$C. Calculate its theoretical maximum efficiency.

Q83.

A Carnot engine operates between a hot reservoir at 156$^\circ$C and a cold sink at 40$^\circ$C. Calculate its theoretical maximum efficiency.

Q84.

A Carnot engine operates between a hot reservoir at 157$^\circ$C and a cold sink at 37$^\circ$C. Calculate its theoretical maximum efficiency.

Q85.

A Carnot engine operates between a hot reservoir at 219$^\circ$C and a cold sink at 35$^\circ$C. Calculate its theoretical maximum efficiency.

Q86.

A Carnot engine operates between a hot reservoir at 140$^\circ$C and a cold sink at 40$^\circ$C. Calculate its theoretical maximum efficiency.

Q87.

A Carnot engine operates between a hot reservoir at 229$^\circ$C and a cold sink at 40$^\circ$C. Calculate its theoretical maximum efficiency.

Q88.

A Carnot engine operates between a hot reservoir at 271$^\circ$C and a cold sink at 44$^\circ$C. Calculate its theoretical maximum efficiency.

Q89.

A Carnot engine operates between a hot reservoir at 102$^\circ$C and a cold sink at 25$^\circ$C. Calculate its theoretical maximum efficiency.

Q90.

A Carnot engine operates between a hot reservoir at 208$^\circ$C and a cold sink at 22$^\circ$C. Calculate its theoretical maximum efficiency.

Topic 10: Second Law Concepts & Entropy

Q91.

An isothermal reservoir at 300 K supplies 2512 J of heat to a reversible engine. What is the change in entropy of the reservoir?

Q92.

An isothermal reservoir at 273 K supplies 4292 J of heat to a reversible engine. What is the change in entropy of the reservoir?

Q93.

An isothermal reservoir at 300 K supplies 3059 J of heat to a reversible engine. What is the change in entropy of the reservoir?

Q94.

An isothermal reservoir at 273 K supplies 2506 J of heat to a reversible engine. What is the change in entropy of the reservoir?

Q95.

An isothermal reservoir at 273 K supplies 1532 J of heat to a reversible engine. What is the change in entropy of the reservoir?

Q96.

An isothermal reservoir at 373 K supplies 3203 J of heat to a reversible engine. What is the change in entropy of the reservoir?

Q97.

An isothermal reservoir at 300 K supplies 1343 J of heat to a reversible engine. What is the change in entropy of the reservoir?

Q98.

An isothermal reservoir at 373 K supplies 4049 J of heat to a reversible engine. What is the change in entropy of the reservoir?

Q99.

An isothermal reservoir at 300 K supplies 2638 J of heat to a reversible engine. What is the change in entropy of the reservoir?

Q100.

An isothermal reservoir at 273 K supplies 3852 J of heat to a reversible engine. What is the change in entropy of the reservoir?