The specific heat capacities of an ideal gas | vedclass

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Question

(D) Given,specific heat capacity at constant pressure,$C_p = 620 \ J \ kg^{-1} \ K^{-1}$ and specific heat capacity at constant volume,$C_v = 420 \ J

Vedclass · Accepted Answer

$1.86$

Vedclass · Answer

(D) Given,specific heat capacity at constant pressure,$C_p = 620 \ J \ kg^{-1} \ K^{-1}$ and specific heat capacity at constant volume,$C_v = 420 \ J \ kg^{-1} \ K^{-1}$.The molar mass $M$ of the gas is related to the gas constant $R$ by the relation: $M(C_p - C_v) = R$.Substituting the values: $M(620 - 420) = 8.314 \ J \ mol^{-1} \ K^{-1}$.$M(200) = 8.314 \implies M = \frac{8.314}{200} = 0.04157 \ kg \ mol^{-1}$.At $STP$,pressure $P = 1.013 	imes 10^5 \ Pa$ and temperature $T = 273.15 \ K$.Using the ideal gas equation $PV = nRT = \frac{m}{M}RT$,we get the density $ho = \frac{m}{V} = \frac{PM}{RT}$.$ho = \frac{(1.013 	imes 10^5) 	imes 0.04157}{8.314 	imes 273.15} \approx 1.855 \ kg \ m^{-3}$.Rounding to the nearest value,we get $ho \approx 1.86 \ kg \ m^{-3}$.Therefore,option $(D)$ is correct.

	Gases		$C_P/C_V$ value
$A$	Monoatomic	$I$	$(4+f)/(3+f)$
$B$	Diatomic (rigid)	$II$	$5/3$
$C$	Diatomic (non-rigid)	$III$	$7/5$
$D$	Polyatomic	$IV$	$9/7$

The specific heat capacities of an ideal gas at constant pressure and at constant volume are $620 \ J \ kg^{-1} \ K^{-1}$ and $420 \ J \ kg^{-1} \ K^{-1}$ respectively. The density of the gas at $STP$ is approximately, (in $kg \ m^{-3}$)

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$C$ Diatomic (non-rigid) $III$ $7/5$

$D$ Polyatomic $IV$ $9/7$

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