To increase the temperature of 1 mole of an i | vedclass

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(A) At constant pressure,the heat supplied is given by $(\Delta Q)_P = n C_P \Delta T$.Given $n = 1 \, mole$,$\Delta T = (30 - 20) = 10^{\circ}C$,and

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$20$

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(A) At constant pressure,the heat supplied is given by $(\Delta Q)_P = n C_P \Delta T$.Given $n = 1 \, mole$,$\Delta T = (30 - 20) = 10^{\circ}C$,and $(\Delta Q)_P = 40 \, cal$.Substituting these values: $40 = 1 	imes C_P 	imes 10$,which gives $C_P = 4 \, cal/(mol \cdot K)$.For an ideal gas,the relationship between molar heat capacities is $C_P - C_V = R$.Given $R \approx 2 \, cal/(mol \cdot K)$,we have $C_V = C_P - R = 4 - 2 = 2 \, cal/(mol \cdot K)$.At constant volume,the heat required is $(\Delta Q)_V = n C_V \Delta T$.Substituting the values: $(\Delta Q)_V = 1 	imes 2 	imes 10 = 20 \, cal$.

	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	$IV$	$9/7$

To increase the temperature of $1$ mole of an ideal monatomic gas by $10^{\circ}C$ at constant pressure,$40 \, cal$ of heat is required. How much heat (in $cal$) is required to increase the temperature by the same amount at constant volume?

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