Five moles of an ideal gas are heated at constant volume from 10°C to 20°C. The molar heat capacity at constant pressure is Cₚ = 8 cal·mol⁻¹·°C⁻¹ and the gas constant is R = 8.36 J·mol⁻¹·°C⁻¹. Taking 1 cal = 4.18 J, find the change in internal energy in calories.
Physics · Thermodyanmics · thermodynmic process and work done
JEE Mains 2026 2 April Evening Shift

Question

Five moles of an ideal gas are heated at constant volume from 10°C to 20°C. The molar heat capacity at constant pressure is Cₚ = 8 cal·mol⁻¹·°C⁻¹ and the gas constant is R = 8.36 J·mol⁻¹·°C⁻¹. Taking 1 cal = 4.18 J, find the change in internal energy in calories.

Physics · Thermodyanmics · thermodynmic process and work done

JEE Mains 2026 2 April Evening Shift

G1 Physics · Accepted Answer

For an ideal gas, Cₚ-Cᵥ = R. Convert R to calorie units: R = 8.36 J·mol⁻¹·°C⁻¹ = 8.36 ÷ 4.18 = 2 cal·mol⁻¹·°C⁻¹. Therefore, Cᵥ = Cₚ-R = 8-2 = 6 cal·mol⁻¹·°C⁻¹. The temperature rise is ΔT = 20-10 = 10°C. At constant volume, ΔU = nCᵥΔT. Thus, ΔU = 5×6×10 = 300 cal. Therefore the answer is 300.