First Law Of Thermodynamics - UNSOLVED PRACTICE SET
Chapter: Thermodynamics | Topic: First Law of Thermodynamics
FIRST LAW OF THERMODYNAMICS - UNSOLVED PRACTICE SET
Topic: First Law of Thermodynamics
Multiple Choice Questions
Q1. The First Law of Thermodynamics is essentially the law of:
- Conservation of momentum
- Conservation of energy
- Conservation of mass
- Conservation of charge
Q2. For a system undergoing an adiabatic process, the First Law reduces to:
- ΔU = Q
- ΔU = –W
- ΔU = W
- ΔU = 0
Q3. In a process where Q = 0 and W = 0, the change in internal energy is:
- Positive
- Negative
- Zero
- Infinite
Q4. A gas absorbs 100 J of heat and does 40 J of work. The change in internal energy is:
- 140 J
- 60 J
- –60 J
- –140 J
Q5. The First Law of Thermodynamics for a cyclic process becomes:
- Q = W
- Q = –W
- Q = ΔU
- ΔU = W
Q6. When you vigorously rub your hands together on a cold morning, they become warm. This is an example of:
- Heat transfer increasing internal energy
- Work done increasing internal energy
- Adiabatic cooling
- Isothermal expansion
Short Answer Questions
Q7. State the First Law of Thermodynamics mathematically and explain each term with proper sign convention.
Q8. A system absorbs 500 J of heat and its internal energy increases by 300 J. How much work is done by the system? Show your calculation.
Q9. Explain why the First Law of Thermodynamics does not forbid the existence of a perpetual motion machine of the first kind (PMM-1).
Q10. In an isothermal process for an ideal gas, what happens to the heat supplied? How does the First Law explain this?
Q11. Distinguish between an adiabatic wall and a diathermic wall. How does each affect the application of the First Law?
Q12. A closed system undergoes a process where 200 J of work is done on the system and the system releases 150 J of heat to the surroundings. Calculate the change in internal energy.
Long Answer Questions
Q13. State the First Law of Thermodynamics. Explain its physical significance and show how it is a statement of the law of conservation of energy. Discuss the sign conventions used for heat, work, and internal energy in detail.
Q14. Consider the following processes applied to one mole of an ideal monoatomic gas:
(i) The gas is heated at constant volume, temperature rising from T₁ to T₂
(ii) The gas expands isothermally from V₁ to V₂
(iii) The gas is compressed adiabatically from V₂ to V₁
For each process, apply the First Law to find:
The heat exchanged (Q)
The work done (W)
The change in internal energy (ΔU)
Q15. A student claims that if a system returns to its initial state after a cyclic process, then no net heat was absorbed and no net work was done. Is this statement correct? Use the First Law to analyze cyclic processes and explain why a heat engine can produce net work in a cycle.
Numerical / Application-Based Problems
Q16. A gas is taken through a cyclic process ABCDA as shown in the P-V diagram. The values at the corners are:
A: P = 1 × 10⁵ Pa, V = 1 × 10⁻³ m³
B: P = 2 × 10⁵ Pa, V = 1 × 10⁻³ m³
C: P = 2 × 10⁵ Pa, V = 3 × 10⁻³ m³
D: P = 1 × 10⁵ Pa, V = 3 × 10⁻³ m³
Calculate:
(i) Work done in each process (AB, BC, CD, DA)
(ii) Net work done in the cycle
(iii) Net heat exchanged in the cycle
(iv) Change in internal energy for the complete cycle
Q17. One mole of an ideal monoatomic gas at 300 K is heated at constant pressure until its volume doubles.
(i) Calculate the final temperature of the gas.
(ii) Calculate the work done by the gas.
(iii) Calculate the heat supplied to the gas.
(iv) Calculate the change in internal energy.
(v) Verify your answers using the First Law of Thermodynamics.
(Given: R = 8.31 J mol⁻¹ K⁻¹)
Q18. A rigid container of volume 2 × 10⁻³ m³ contains 0.1 moles of an ideal diatomic gas at 300 K. An electric heater supplies 500 J of energy to the gas.
(i) Calculate the change in temperature of the gas.
(ii) Calculate the final pressure of the gas.
(iii) How much work is done by the gas? Explain.
(iv) Verify the First Law for this process.
(Given: R = 8.31 J mol⁻¹ K⁻¹)