Ideal diatomic gas is taken through a process ΔQ = 2ΔU. If the molar heat capacity (in J/K ) for the process is x, then find the value of 10x. (Where ΔQ is the heat supplied and ΔU is change in internal energy)
Physics · Thermodynamics
JEE Mains

Question

Ideal diatomic gas is taken through a process ΔQ = 2ΔU. If the molar heat capacity (in J/K ) for the process is x, then find the value of 10x. (Where ΔQ is the heat supplied and ΔU is change in internal energy)

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 416.