Question

70 cal of heat is required to raise the temperature of 2 moles of an ideal gas at constant pressure from 30°C to 35°C. The amount of heat required to raise the temperature of the gas through the same range at constant volume will be (assume R = 2 cal/mol-K).

Options

• 30 cal

• 50 cal

• 70 cal

• 90 cal

Answer 1

50 cal

Explanation:

Q_P = heat needed at constant pressure = nC_p Δt

Q_v = heat required at constant volume = nC_v Δt

Q_P = 70 = 2 × C_p × (35° - 30°)

Now, C_P = 7 cal/mol-K

C_P - C_v = R

So, 7 - C_v = 2 ⇒ C_v = 5 col/mol-k

Q_v = nC_v Δt = 2 × 5 × (35° - 30°) = 50 cal