Internal Energy & Work - UNSOLVED PRACTICE SET

Q7. Define internal energy of a thermodynamic system. Is it a state function or a path function? Justify.

Q8. Distinguish between work done by the system and work done on the system. How does the sign convention differentiate them?

Q9. Explain why the internal energy of an ideal gas depends only on its temperature, while for a real gas, it may depend on both temperature and volume.

Q10. A gas is compressed from volume V₁ to V₂ at constant pressure P. Write the expression for work done and state whether it is positive or negative.

Q11. What is meant by a state function? Give two examples of state functions and two examples of path functions in thermodynamics.

Q12. In a P-V diagram, how is the work done by a gas represented graphically? Explain for both expansion and compression.

Q13. Derive the expression for work done by an ideal gas during isothermal expansion from volume V₁ to V₂. Explain why the work done depends on the path taken, even though internal energy change is zero.

Q14. Describe the molecular interpretation of internal energy for an ideal gas. Explain how translational, rotational, and vibrational degrees of freedom contribute to the internal energy. How does this explain why U = (f/2)nRT, where f is the degrees of freedom?

Q15. A gas undergoes a cyclic process shown on a P-V diagram as a closed loop. The loop is traversed clockwise.

(i) What is the net change in internal energy after one complete cycle?

(ii) What does the area enclosed by the loop represent?

(iii) If the loop is traversed counter-clockwise, how does the work done change?

Q16. One mole of an ideal monoatomic gas is taken from state A (P_A = 2 × 10⁵ Pa, V_A = 2 × 10⁻³ m³) to state B (P_B = 4 × 10⁵ Pa, V_B = 4 × 10⁻³ m³) along two different paths:

Path 1: First isobaric expansion to V_B, then isochoric pressure change to P_B

Path 2: First isochoric pressure change to P_B, then isobaric expansion to V_B

Calculate:

(i) Work done along Path 1

(ii) Work done along Path 2

(iii) Change in internal energy for both paths

(iv) What conclusion can you draw about work and internal energy?

Q17. A cylinder contains 0.5 moles of an ideal diatomic gas at 300 K. The gas is heated at constant volume until its temperature rises to 400 K.

(i) Calculate the change in internal energy of the gas.

(ii) Calculate the work done by the gas.

(iii) Explain why the work done has this value.

(iv) If the same gas were heated from 300 K to 400 K at constant pressure, would the change in internal energy be different? Explain.

(Given: R = 8.31 J mol⁻¹ K⁻¹)

Q18. The P-V diagram shows a process ABC for 2 moles of an ideal gas. The pressure at A is 1 × 10⁵ Pa and volume is 2 × 10⁻³ m³. At B, volume is 4 × 10⁻³ m³ at the same pressure. At C, pressure is 2 × 10⁵ Pa at the same volume as B.

(i) Calculate the work done in process AB.

(ii) Calculate the work done in process BC.

(iii) Calculate the total work done in process ABC.

(iv) If the temperature at A is 300 K, find the temperature at C.