P-V diagram of an ideal diatomic gas is a straight line passing through origin. The molar heat capacity of the gas in the process is x R. Find x. (Here R= Universal gas constant)

Question

P-V diagram of an ideal diatomic gas is a straight line passing through origin. The molar heat capacity of the gas in the process is x R. Find x. (Here R= Universal gas constant) (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

P-V graph is a straight line passing through origin. ∴ P propto V P V-1= Constant Polytropic index, m=-1 C=(R/&gamma;-1)+(R/-m+1) C=(R/1.4-1)+(R/1-(-1))=x R ∴ x=3

Q. $P - V$ diagram of an ideal diatomic gas is a straight line passing through origin. The molar heat capacity of the gas in the process is $x R$ . Find $x$ . (Here $R =$ Universal gas constant)

$P - V$ graph is a straight line passing through origin.
$∴ P \propto V$
$P V^{- 1} =$ Constant
Polytropic index, $m = - 1$
$C = \frac{R}{γ - 1} + \frac{R}{- m + 1}$
$C = \frac{R}{1.4 - 1} + \frac{R}{1 - ( - 1 )} = x R$
$∴ x = 3$

Q. P−V diagram of an ideal diatomic gas is a straight line passing through origin. The molar heat capacity of the gas in the process is xR. Find x. (Here R= Universal gas constant)

P−V graph is a straight line passing through origin. ∴P∝V PV−1= Constant Polytropic index, m=−1 C=γ−1R​+−m+1R​ C=1.4−1R​+1−(−1)R​=xR ∴x=3

Q. $P - V$ diagram of an ideal diatomic gas is a straight line passing through origin. The molar heat capacity of the gas in the process is $x R$ . Find $x$ . (Here $R =$ Universal gas constant)

$P - V$ graph is a straight line passing through origin.
$∴ P \propto V$
$P V^{- 1} =$ Constant
Polytropic index, $m = - 1$
$C = \frac{R}{γ - 1} + \frac{R}{- m + 1}$
$C = \frac{R}{1.4 - 1} + \frac{R}{1 - ( - 1 )} = x R$
$∴ x = 3$