For a gas having molar mass M, specific heat at constant pressure per gram of gas is given by

Question

For a gas having molar mass M, specific heat at constant pressure per gram of gas is given by (A) (&gamma; R/M(&gamma;-1)) (B) (&gamma;/R M) (C) (M/R(&gamma;-1)). (D) (&gamma; R M/(&gamma;+1))

Tardigrade Admin · Accepted Answer

Cp-Cv=R and (Cp/Cv)=&gamma; ∴ Cp-(Cp/&gamma;)=R or Cp((&gamma;-1/&gamma;))=R or Cp=(R &gamma;/(&gamma;-1))=M barCp or barCp=(&gamma; R/M(&gamma;-1))

Q. For a gas having molar mass $M,$ specific heat at constant pressure per gram of gas is given by

$\frac{γ R}{M ( γ - 1 )}$

$\frac{γ}{RM}$

$\frac{M}{R ( γ - 1 )}$ .

$\frac{γ RM}{( γ + 1 )}$

$C_{p} - C_{v} = R$ and $\frac{C _{p}}{C _{v}} = γ$

$∴ C_{p} - \frac{C _{p}}{γ} = R$ or $C_{p} (\frac{γ - 1}{γ}) = R$

or $C_{p} = \frac{R γ}{( γ - 1 )} = M \overset{ˉ}{C}_{p}$ or $\overset{ˉ}{C}_{p} = \frac{γ R}{M ( γ - 1 )}$

Q. For a gas having molar mass M, specific heat at constant pressure per gram of gas is given by

M(γ−1)γR​

RMγ​

R(γ−1)M​.

(γ+1)γRM​