When 300 J of heat given to an ideal gas with Cₚ = 7R/2 its temperature raises from 20°C to 50°C keeping its volume constant. The mass of the gas is (approximately) ___ g. (R = 8.314 J/mol·K).
Physics · Thermodyanmics · thermodynmic process and work done
JEE Mains 2026 24 January Evening Shift

Question

When 300 J of heat given to an ideal gas with Cₚ = 7R/2 its temperature raises from 20°C to 50°C keeping its volume constant. The mass of the gas is (approximately) ___ g. (R = 8.314 J/mol·K).

G1 Physics · Accepted Answer

At constant volume, Q = nCᵥΔT. Given, Cₚ = 7R/2. Therefore, Cᵥ = Cₚ-R = 5R/2. The temperature rise is ΔT = 50-20 = 30 K. Hence, 300 = n(5R/2)(30). Substitute R = 8.314 J·mol⁻¹·K⁻¹. Therefore, n = 300/ [(5/2)(8.314)(30)] ≈ 0.481 mol. However, the question asks for mass in grams. Mass is m = nM, where M is the molar mass of the gas. The molar mass is not given in the question, so the mass cannot be uniquely determined from the supplied data. The source lists NTA answer 481 and Allen marks the que…