Heat & Thermodynamics

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Q1. If 2000 J of heat is added to a system and 500 J of work is done by the system, what is the change in internal energy of the system? (2021)

Solution:

Using the first law of thermodynamics: ΔU = Q - W = 2000 J - 500 J = 1500 J.

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Q2. A 1 kg block of ice at 0°C is placed in 2 kg of water at 20°C. What will be the final temperature of the mixture? (Specific heat of water = 4.2 kJ/kg°C, Latent heat of fusion of ice = 334 kJ/kg) (2021)

Solution:

Heat lost by water = Heat gained by ice. Calculate to find the final temperature.

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Q3. What is the change in internal energy of a system if 200 J of heat is added and 50 J of work is done by the system?

Solution:

Using the first law of thermodynamics, ΔU = Q - W = 200 J - 50 J = 150 J.

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Q4. A refrigerator removes heat from the inside at a rate of 200 J/s and expels it to the surroundings at a rate of 250 J/s. What is the coefficient of performance (COP) of the refrigerator? (2023)

Solution:

COP = Q_in / W = 200 J/s / (250 J/s - 200 J/s) = 200 / 50 = 4.

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Q5. What is the change in internal energy of a system if 300 J of heat is added and 100 J of work is done by the system? (2021)

Solution:

Using the first law of thermodynamics: ΔU = Q - W = 300 J - 100 J = 200 J.

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Q6. In an adiabatic process, the temperature of an ideal gas decreases. What happens to its pressure?

Solution:

In an adiabatic process, as the temperature decreases, the pressure also decreases due to the ideal gas law.

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Q7. A gas expands isothermally at 300 K from a volume of 1 m³ to 2 m³. If the pressure of the gas is 100 kPa, what is the work done by the gas? (2020)

Solution:

Work done (W) = P * ΔV = 100 kPa * (2 m³ - 1 m³) = 100 kPa * 1 m³ = 100 kJ = 10 kJ.

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Q8. What is the latent heat of vaporization of water if 540 J of energy is required to convert 100 g of water at 100°C to steam? (2021)

Solution:

Latent heat of vaporization (L) = Q/m = 540 J / 100 g = 5.4 J/g.

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Q9. 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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Q10. What is the final temperature when 200 g of ice at 0°C is added to 100 g of water at 80°C? (Specific heat of water = 4.2 J/g°C) (2020)

Solution:

Using the principle of conservation of energy, the heat lost by water equals the heat gained by ice. Solving gives a final temperature of 20°C.

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