A quantity of 56 g of nitrogen gas is enclosed in a rigid vessel at a temperature 300 K. The amount of heat (in kcal) has to be transferred to the gas to increase the root mean square velocity of its

Question

A quantity of 56 g of nitrogen gas is enclosed in a rigid vessel at a temperature 300 K. The amount of heat (in kcal) has to be transferred to the gas to increase the root mean square velocity of its molecules 2.0 times is

TestHub · Accepted Answer

v r ms ∝ √T, so doubling v r ms needs T₂ = 4T₁ = 1200 K, ΔT = 900 K. Rigid vessel ⇒ isochoric: Q = nC v ΔT. n = 56/28 = 2 mol; N₂ diatomic, C v = (5/2)R = 5 cal K⁻¹ mol⁻¹. Q = 2 × 5 × 900 = 9000 cal = 9 kcal.

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