A quantity of 28 g of carbon monoxide gas is enclosed in a rigid vessel at a temperature 400 K. The amount of heat (in kcal) that has to be transferred to the gas to increase the root mean square velo

Question

A quantity of 28 g of carbon monoxide gas is enclosed in a rigid vessel at a temperature 400 K. The amount of heat (in kcal) that 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 requires T₂ = 4T₁ = 1600 K, ΔT = 1200 K (not 2T₁ - the trap is forgetting the square). Rigid vessel ⇒ isochoric: Q = nC v ΔT. n = 28/28 = 1 mol (CO, M = 28 g mol⁻¹); CO is diatomic, C v = (5/2)R = 5 cal K⁻¹ mol⁻¹. Q = 1 × 5 × 1200 = 6000 cal = 6 kcal.

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