The specific heat of a gas at constant pressu | vedclass

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(A) By the first law of thermodynamics,$dQ = dU + dW$.For a gas at constant volume,the volume change $dV = 0$,so the work done $dW = P dV = 0$. Thus,a

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work is done in the expansion of the gas at constant pressure

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(A) By the first law of thermodynamics,$dQ = dU + dW$.For a gas at constant volume,the volume change $dV = 0$,so the work done $dW = P dV = 0$. Thus,all heat supplied goes into increasing the internal energy $(dQ = dU = C_v dT)$.For a gas at constant pressure,when heat is supplied,the gas expands to maintain constant pressure. This expansion requires the gas to do work against the external pressure $(dW = P dV > 0)$.Therefore,to achieve the same rise in temperature $(dT)$,more heat must be supplied at constant pressure to account for both the increase in internal energy and the work done during expansion $(C_p dT = dU + P dV)$.Since $C_p dT > C_v dT$,it follows that $C_p > C_v$.

	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 of a gas at constant pressure $(C_p)$ is more than that of the same gas at constant volume $(C_v)$ because

Similar Questions

$A$ polyatomic gas has $f$ vibrational degrees of freedom, then the ratio of the specific heat at constant pressure to that at constant volume will be

Match the following ( $f$ is number of degrees of freedom):

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 $IV$ $9/7$

$A$ diatomic gas is heated at constant pressure. What fraction of the heat energy is used to increase the internal energy?

$Assertion :$ The ratio of $\frac{C_p}{C_v}$ for an ideal diatomic gas is less than that for an ideal monoatomic gas (where $C_p$ and $C_v$ have usual meaning).
$Reason :$ The atoms of a monoatomic gas have less degrees of freedom as compared to molecules of the diatomic gas.

The specific heat of a gas is:

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