Question

When a certain perfect gas is heated at constant pressure fr 15 degree C to 95 degree C, the heat required is 1136KJ/Kg.When the same gas is heated at constant volume between the same temperatures the heat required is 808KJ/Kg. Calculate the Cp, Cv, R and molar mass of the gas.

Answer 1

$T 1 ​ =15°$

$T 2 ​ =95°$

$ΔQ _1 ​ =1136 kg/ kJ$

$ΔQ _2 ​ =808 kg/ kJ ​$

$ΔQ _1 ​ =c _p ​ ΔT→c _p ​ = ΔQ _1/ΔT ​ ​ = 1136000/80 ​ = 14200 J/kgK$

$ΔQ _2 ​ =c _v ​ ΔT→c _v ​ = ΔQ _1/ΔT ​ ​ = 808000/80 ​ = 10100 J/kgK$

$γ= ​ c _p/c_v ​ ​ = 14200/10100 ​ =1.4$

$R _m ​ =c _p ​ −c _V ​ =14200−10100=4100 J/ kg⋅K ​$

$R=R _m ​ ⋅M→M= R/R _m ​ ​ = 8.31/4100 ​ =0.002 kg/mol$

The gas is hydrogen $(H_2)$