10 mole of oxygen is heated at constant volume from 30°C to 40°C. The change in the internal energy of the gas i s _______ cal. (The molecular specific heat of oxygen at constant pressure, Cₚ = 7 cal.·mol⁻¹·°C⁻¹ and R = 2 cal.·mol⁻¹·°C⁻¹.)
Physics · Thermodyanmics · kinetic therory of gaseous
JEE Mains 2026 21 January Morning Shift

Question

10 mole of oxygen is heated at constant volume from 30°C to 40°C. The change in the internal energy of the gas i s _______ cal. (The molecular specific heat of oxygen at constant pressure, Cₚ = 7 cal.·mol⁻¹·°C⁻¹ and R = 2 cal.·mol⁻¹·°C⁻¹.)

Physics · Thermodyanmics · kinetic therory of gaseous

JEE Mains 2026 21 January Morning Shift

G1 Physics · Accepted Answer

For an ideal gas, Cᵥ = Cₚ-R. Given, Cₚ = 7 cal·mol⁻¹·°C⁻¹, R = 2 cal·mol⁻¹·°C⁻¹. Therefore, Cᵥ = 7-2 = 5 cal·mol⁻¹·°C⁻¹. The temperature rise is ΔT = 40-30 = 10°C. At constant volume, ΔU = nCᵥΔT. Thus, ΔU = 10×5×10 = 500 cal. Hence the answer is 500.