Isothermal Adiabatic Isochoric Isobaric Processes - UNSOLVED PRACTICE SET
Chapter: Thermodynamics | Topic: Isothermal Adiabatic Isochoric Isobaric Processes
ISOTHERMAL ADIABATIC ISOCHORIC ISOBARIC PROCESSES - UNSOLVED PRACTICE SET
Topic: Isothermal Adiabatic Isochoric Isobaric Processes
Multiple Choice Questions
Q1. In an isothermal process, the product of pressure and volume for an ideal gas is:
- Variable
- Constant
- Zero
- Infinite
Q2. For an adiabatic process involving an ideal gas, which relation is correct?
- TV^(γ–1) = constant
- TV^γ = constant
- T^γ V = constant
- TV = constant
Q3. In an isochoric process, the work done by the gas is:
- Positive
- Negative
- Zero
- Depends on the gas
Q4. During an isobaric expansion of an ideal gas, the ratio of work done to heat supplied is
- 1/γ
- (γ – 1)/γ
- γ/(γ – 1)
- 1/(γ – 1)
Q5. The slope of an adiabatic curve on a P-V diagram is __________ the slope of an isothermal curve at the same point.
- Equal to
- Less than
- Greater than
- Unrelated to
Q6. When you quickly open a bottle of cold drink on a hot summer day, the gas escaping from the bottle undergoes approximately:
- An isothermal process
- An isobaric process
- An adiabatic process
- An isochoric process
Short Answer Questions
Q7. Write the conditions required for a process to be isothermal. Why must the process be carried out very slowly?
Q8. Explain why an adiabatic process is also called an isentropic process for a reversible adiabatic change.
Q9. Draw a P-V diagram showing isothermal and adiabatic curves starting from the same initial state. Which curve is steeper? Explain why.
Q10. In an isobaric process, why does the temperature of the gas change even though the pressure remains constant?
Q11. A gas is heated at constant volume. Explain what happens to its pressure and temperature using the ideal gas equation.
Q12. Why is it impossible to achieve a perfectly isothermal or perfectly adiabatic process in practice? Give one practical limitation for each.
Long Answer Questions
Q13. Derive the equation PV^γ = constant for an adiabatic process involving an ideal gas. Starting from the First Law and the ideal gas equation, show all steps clearly. Also derive the alternate forms: TV^(γ–1) = constant and P^(1–γ) T^γ = constant.
Q14. Compare and contrast the four thermodynamic processes — isothermal, adiabatic, isochoric, and isobaric — on the following basis:
(i) Conditions required
(ii) Mathematical relation between P, V, and T
(iii) Work done expression
(iv) Change in internal energy
(v) Heat exchange
(vi) P-V diagram representation
Present your answer in a clear tabular format.
Q15. One mole of an ideal monoatomic gas is taken from state A to state B via two different paths:
Path 1: Isothermal expansion from A to B
Path 2: Adiabatic expansion from A to an intermediate state C, followed by isochoric heating to B
Given that T_A = T_B and V_B > V_A:
(i) Sketch the P-V diagram for both paths.
(ii) In which path is more work done? Explain.
(iii) In which path is heat supplied? Explain.
(iv) Compare the final pressures in both cases.
Numerical / Application-Based Problems
Q16. Two moles of an ideal diatomic gas (γ = 7/5) at 300 K are compressed adiabatically to half its original volume.
(i) Calculate the final temperature of the gas.
(ii) Calculate the work done on the gas.
(iii) Calculate the change in internal energy.
(iv) Verify that the First Law is satisfied.
(Given: R = 8.31 J mol⁻¹ K⁻¹)
Q17. A cylinder fitted with a movable piston contains 1 mole of an ideal monoatomic gas at 1 × 10⁵ Pa and 300 K. The gas is first heated isobarically until its volume doubles, and then heated isochorically until its pressure doubles.
(i) Calculate the temperature after the isobaric process.
(ii) Calculate the temperature after the isochoric process.
(iii) Calculate the total work done by the gas.
(iv) Calculate the total heat supplied to the gas.
(v) Sketch the P-V diagram for the complete process.
(Given: R = 8.31 J mol⁻¹ K⁻¹)
Q18. A bicycle pump is used to inflate a tire. The air in the pump cylinder is compressed rapidly (assume adiabatically) from an initial volume of 200 cm³ at atmospheric pressure (1 × 10⁵ Pa) and 27°C to a final volume of 50 cm³. The air can be treated as an ideal diatomic gas (γ = 7/5).
(i) Calculate the final temperature of the air in the pump.
(ii) Calculate the final pressure of the air.
(iii) Calculate the work done on the air.
(iv) Explain why the pump becomes warm during this process.
(v) If the compression were done very slowly (isothermally), how would the final pressure and temperature differ?