Khimraj
Last Activity: 7 Years ago
ΔQ1 = n C_v ΔT
= n C_v (2T1 - T1) = n C_v * T1
ΔQ2 = n C_p ΔT = n C_p * (4T1 - 2T1) = 2 n C_p T1
= 2 n γ C_v T1
ΔQ1 + ΔQ2 = n C_v T1 + 2 n γ C_v T1 = n T1 (1 + 2 γ) C_v
C_m = [ ΔQ1 + ΔQ2 ] / [ n ΔT ]
C_m = [ n T1 (1 + 2 γ) C_v ] / [ n 3 T1 ]
= (1 + 2 γ) C_v / 3
For monoatomic gas
C_v = 5/2R
γ = 5/3.
So C_m = (1 + 10/3)*(3/2R)/3 = 13R/6.
Hope it clears.