Q1. If the volume of a gas is halved at constant temperature, what happens to its pressure? (2023)
Solution:
According to Boyle's Law, if the volume is halved, the pressure doubles at constant temperature.
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Q2. In a Carnot engine operating between temperatures of 500 K and 300 K, what is the maximum efficiency? (2023)
Solution:
Efficiency (η) = 1 - (T_cold / T_hot) = 1 - (300 K / 500 K) = 0.4 or 40%.
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Q3. A 100 g piece of metal at 100°C is placed in 200 g of water at 20°C. What will be the final temperature of the system? (Specific heat of water = 4.2 J/g°C, specific heat of metal = 0.5 J/g°C) (2023)
Solution:
Using the heat transfer equation, we can find the final temperature to be 50°C.
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Q4. If 200 J of heat is added to a system and 50 J of work is done by the system, what is the change in internal energy? (2023)
Solution:
According to the first law of thermodynamics, ΔU = Q - W = 200 J - 50 J = 150 J.
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Q5. A 1 kg block of metal at 100°C is placed in 2 kg of water at 20°C. What is the final temperature of the system? (Specific heat of water = 4.18 J/g°C, specific heat of metal = 0.9 J/g°C) (2021)
Solution:
Using conservation of energy: m1*c1*(T_initial - T_final) = m2*c2*(T_final - T_initial). Solving gives T_final = 35°C.
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Q6. If the latent heat of fusion of ice is 334 J/g, how much heat is required to melt 50 g of ice? (2019)
Solution:
Heat required = mass × latent heat = 50 g × 334 J/g = 16700 J.
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Q7. What is the efficiency of a Carnot engine operating between 300 K and 600 K? (2022)
Solution:
Efficiency = 1 - (T_c/T_h) = 1 - (300/600) = 0.5.
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Q8. In a Carnot engine operating between 500 K and 300 K, what is the maximum efficiency of the engine? (2021)
Solution:
Efficiency (η) = 1 - (T_cold / T_hot) = 1 - (300 K / 500 K) = 0.4 or 40%.
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Q9. What is the specific heat capacity of a substance if it requires 500 J to raise the temperature of 2 kg of the substance by 10°C? (2021)
Q10. A 1 kg block of ice at 0°C is placed in 2 kg of water at 80°C. What will be the final temperature of the mixture? (Assume no heat loss to the surroundings) (2019)
Solution:
Using the principle of conservation of energy, the heat lost by water equals the heat gained by ice. The final temperature will be 0°C as the ice will melt.
