If Cₚ and Cᵥ denote the specific heats per unit mass of an ideal gas of molecular weight M, then (R is the molar gas constant):
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Question

If Cₚ and Cᵥ denote the specific heats per unit mass of an ideal gas of molecular weight M, then (R is the molar gas constant):

G1 Physics · Accepted Answer

Step 1: For an ideal gas, Mayer's relation for MOLAR heat capacities is Cₚ − Cᵥ = R. Step 2: Each mass-specific heat capacity equals the corresponding molar heat capacity divided by molar mass M. Step 3: Therefore, the mass-specific difference is (Cₚ − Cᵥ)/M = R/M when the symbols in the numerator refer to molar capacities. Step 4: The question uses Cₚ and Cᵥ for mass-specific heat capacities, so in its notation the result is Cₚ − Cᵥ = R/M. Final answer: (C) R/M. Use units for M consistent with…