A system absorbs 8000 J of heat and its internal energy increases by 5000 J. According to the first law of thermodynamics, what work is done by the system?
Answer: A
First law: ΔU = Q - W, so W = Q - ΔU = 8000 - 5000 = 3000 J (work done by the system)
Q.82Hard
For an ideal gas undergoing a polytropic process (PV^n = constant), the heat capacity is C = C_v + R/(1-n). For which value of n does the polytropic process become adiabatic?
Answer: B
For adiabatic process, Q = 0, so C = 0. This occurs when 1-n approaches infinity, which happens when n = γ. At n = γ, PV^γ = constant (adiabatic relation).
Q.83Medium
A thermally insulated container holds 2 moles of oxygen gas at 300 K. A heating element supplies 5000 J of heat to the gas. What is the final temperature? (C_v for O₂ = 5R/2, R = 8.314 J/mol·K)
Answer: C
Q = nC_vΔT. 5000 = 2 × (25) × 8.314 × ΔT. ΔT = 5000/(5 × 8.314) = 415000.57 ≈ 120.2 K. Final T = 300 + 120.2 ≈ 380 K
Q.84Medium
For a Carnot refrigerator operating between 250 K (cold reservoir) and 300 K (hot reservoir), the coefficient of performance (COP) is:
When a system undergoes a process where both Q and W are positive, which statement is true?
Answer: C
From first law: ΔU = Q - W. If both Q and W are positive, ΔU = Q - W could be positive, negative, or zero depending on whether Q > W, Q < W, or Q = W respectively.
Q.87Hard
A gas sample at 300 K has an entropy of 200 J/K. When heated at constant pressure to 600 K, its entropy becomes:
Which thermodynamic process results in maximum work extraction from an ideal gas expanding from the same initial to final states?
Answer: B
For expansion between the same P-V states, isothermal process produces maximum work because W = nRT ln(V_f/V_i) is maximum when temperature is highest throughout the process.
Q.89Easy
A heat engine operates between two reservoirs at temperatures 500 K and 300 K. What is the maximum theoretical efficiency of this engine?
A gas expands isothermally from volume V₁ to 3V₁ at temperature T. If the initial pressure is P₁, what is the work done by the gas?
Answer: A
For isothermal process: W = nRT ln(V_f/V_i) = P₁V₁ ln(3V₁/V₁) = P₁V₁ ln(3)
Q.92Medium
A system undergoes a cyclic process. The internal energy change over one complete cycle is ΔU. Which statement is correct?
Answer: A
Internal energy is a state function, so for a cyclic process where the system returns to its initial state, ΔU = 0 always, regardless of the path.
Q.93Medium
Two identical blocks at different temperatures are brought into thermal contact in an isolated system. Block A at 400 K and Block B at 300 K both have mass 1 kg and specific heat 400 J/kg·K. What is the change in entropy of the universe?
An ideal gas undergoes an adiabatic process from state (P₁, V₁, T₁) to (P₂, V₂, T₂) with γ = 1.4. If volume increases by 50%, the temperature ratio T₂/T₁ is approximately:
A refrigerator operates with a COP (Coefficient of Performance) of 4 between temperatures 250 K and 350 K. What is the theoretical maximum COP possible?
A 2 kg mass of ice at 0°C is mixed with 5 kg of water at 80°C in a thermally insulated container. If latent heat of fusion = 3.36 × 10⁵ J/kg and specific heat of water = 4200 J/kg·K, determine the final state of the system.
Answer: A
Heat available from water cooling from 80°C to 0°C: Q = 5 × 4200 × 80 = 1.68 × 10⁶ J. Heat needed to melt ice: Q = 2 × 3.36 × 10⁵ = 6.72 × 10⁵ J. Since 1.68 × 10⁶ > 6.72 × 10⁵, all ice melts. Remaining heat: 1.68 × 10⁶ - 6.72 × 10⁵ = 1.008 × 10⁶ J raises temperature of 7 kg water: ΔT = 1.008 × 10⁶/(7 × 4200) ≈ 34.3°C → final temp ≈ 34°C
Q.97Hard
A gas sample undergoes a process where pressure decreases linearly with volume: P = P₀ - kV, where k is a constant. For 1 mole of ideal gas at constant temperature, what is the work done when volume changes from V₁ to V₂?
Answer: A
Work done: W = ∫P dV = ∫(P₀ - kV) dV from V₁ to V₂ = [P₀V - kV²/2] from V₁ to V₂ = P₀(V₂ - V₁) - k(V₂² - V₁²)/2
