If cp and cv denote the specific heats (per unit) mass of an ideal gas of molecular weight M, then where R is the molar gas constant.

Question

If cp and cv denote the specific heats (per unit) mass of an ideal gas of molecular weight M, then where R is the molar gas constant. (A) cp-cv =R/M2  (B) cp-cv=R  (C) cp-cv=R/M  (D) cp-cv=MR

Tardigrade Admin · Accepted Answer

Let Cv and Cp be molar specific heats of the ideal gas at constant volume and constant pressure, respectively, then Cp=Mcp and Cv=Mcv CP-CV=R ∴ Mcp-Mcv=R ⇒ cp-cv=R/M

Q. If $c_{p}$ and $c_{v}$ denote the specific heats (per unit) mass of an ideal gas of molecular weight $M$ , then
where $R$ is the molar gas constant.

$c_{p} - c_{v} = R / M^{2}$

$c_{p} - c_{v} = R$

$c_{p} - c_{v} = R / M$

$c_{p} - c_{v} = MR$

Let $C_{v}$ and $C_{p}$ be molar specific heats of the ideal gas at constant volume and constant pressure, respectively, then
$C_{p} = M c_{p}$ and $C_{v} = M c_{v}$
$C_{P} - C_{V} = R$
$∴ M c_{p} - M c_{v} = R$
$\Rightarrow c_{p} - c_{v} = R / M$

Q. If cp​ and cv​ denote the specific heats (per unit) mass of an ideal gas of molecular weight M, then where R is the molar gas constant.

cp​−cv​=R/M2

cp​−cv​=R

cp​−cv​=R/M

cp​−cv​=MR