Internal Energy and Work - UNSOLVED PRACTICE SET
Chapter: Thermodynamics | Topic: Internal Energy and Work
INTERNAL ENERGY AND WORK - UNSOLVED PRACTICE SET
Topic: Internal Energy and Work
Multiple Choice Questions
Q1. Which of the following is the correct expression for the change in internal energy (ΔU) of a system?
- ΔU = q – w
- ΔU = q + w
- ΔU = w – q
- ΔU = q × w
Q2. When work is done by the system on the surroundings, the sign of work (w) is:
- Positive
- Negative
- Zero
- Depends on the process
Q3. For an ideal gas, the internal energy depends only on:
- Pressure and volume
- Volume and temperature
- Temperature alone
- Pressure alone
Q4. In an adiabatic expansion of an ideal gas, which of the following is true?
- q = 0 and ΔU is positive
- q = 0 and ΔU is negative
- q is positive and ΔU = 0
- q is negative and ΔU is positive
Q5. Work done in an isothermal reversible expansion of an ideal gas is given by:
- w = –nR ln(V₂/V₁)
- w = –nRT ln(V₂/V₁)
- w = nRT ln(P₂/P₁)
- w = –nRT ln(P₁/P₂)
Q6. A gas expands against a constant external pressure. The work done by the gas is:
- w = –PΔV
- w = PΔV
- w = –ΔV/P
- w = VΔP
Short Answer Questions
Q7. Define internal energy (U) of a system. Is it a state function or a path function? Justify your answer.
Q8. Explain the sign convention for work done in thermodynamics. When is work done by the system considered negative, and when is work done on the system considered positive?
Q9. Why is the internal energy of an ideal gas a function of temperature only? Explain with reasoning.
Q10. Differentiate between reversible work and irreversible work done during the expansion of a gas. Which one yields more work?
Q11. A gas is compressed isothermally. What happens to its internal energy? Explain your answer.
Q12. Write the expression for work done during an irreversible expansion of an ideal gas against constant external pressure. How does it differ from reversible expansion work?
Long Answer Questions
Q13. (a) Define internal energy and explain why it is an extensive property.
(b) Derive the expression for work done during isothermal reversible expansion of an ideal gas.
(c) A student argues that since internal energy is a state function, the work done by a system must also be a state function. Is the student correct? Explain with reasoning.
Q14. (a) Explain what happens to the internal energy of a system during:
(i) An isothermal process
(ii) An adiabatic process
(iii) An isochoric process
(b) For each case in (a), write the relationship between q, w, and ΔU.
(c) A bicycle pump gets warm when you compress air in it. Explain this observation in terms of internal energy and work.
Q15. (a) Derive the expression for work done in an adiabatic reversible expansion of an ideal gas.
(b) Compare the work done in isothermal reversible expansion and adiabatic reversible expansion of an ideal gas from the same initial state to the same final volume. Which process yields more work? Explain with a P-V diagram description.
Numerical / Application-Based Problems
Q16. Calculate the work done when 2 moles of an ideal gas expand isothermally and reversibly from a volume of 5 L to 15 L at 300 K. (R = 8.314 J/mol·K)
Q17. One mole of an ideal gas at 300 K is compressed isothermally and reversibly from a pressure of 2 atm to 10 atm. Calculate:
(a) The work done on the gas
(b) The change in internal energy (ΔU)
(c) The heat exchanged (q)
(Given: R = 8.314 J/mol·K, ln 5 = 1.609)
Q18. A cylinder contains 5 moles of an ideal gas at 2 atm pressure and 10 L volume. The gas expands against a constant external pressure of 1 atm until its volume becomes 20 L.
(a) Calculate the work done by the gas.
(b) If the process is carried out isothermally, calculate the change in internal energy.
(c) How much heat is absorbed by the gas during this expansion?
(1 L·atm = 101.3 J)