A mixture of 4 g helium and 28 g nitrogen is enclosed at constant volume at 300 K. Heat ΔH is supplied so that the rms speed of the molecules doubles. Find ΔH/1000, with ΔH in joules. Take R as the universal gas constant.
Physics · Thermodynamics
JEE Mains

Question

A mixture of 4 g helium and 28 g nitrogen is enclosed at constant volume at 300 K. Heat ΔH is supplied so that the rms speed of the molecules doubles. Find ΔH/1000, with ΔH in joules. Take R as the universal gas constant.

Physics · Thermodynamics

G1 Physics · Accepted Answer

Use the first law Q=ΔU+W (W by the gas), ΔU=nCᵥΔT for an ideal gas, and the appropriate process relation. For Carnot devices, let T₁ be the cold-reservoir temperature and T₂ be the hot-reservoir temperature; η=1−T₁/T₂ and COP=T₁/(T₂−T₁). Substituting the given values gives 30.