An ideal monoatomic gas undergoes different types of processes which are described in
Column – I. Match the corresponding effects in column – II. The letters have usual meaning.
Column – I Column – II
(a) $P V^{- 2} = c o n s t a n t$ (p) If volume increases then temperature will also increase
(b) $P V^{2} = c o n s t a n t$ (q) If volume increases then temperature will decrease
(C) $C = C_{v} + 2 R$ (r) For expansion, heat will have to be supplied to the gas
(d) $C = C_{v} - 2 R$ (s) If temperature increases then work done by gas is positive
(t) If pressure increases the work done by gas is negative

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a-q,t;b-p,r,s;c-p,q,r,s;d-q,t

a-p,r,s;b-p,s;d-r,s,t;d-p,s

a-p,s;b-q,t;c-r,s,t;d-qt

a-p,r,s;b-q,t;c-p,r,s,t;d-q,t

answer is C.

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Detailed Solution

$f = 3 a) C = \frac{3}{2} R + \frac{R}{3} b) C = \frac{3}{2} R - \frac{R}{3} c) C_{v} + 2 R \frac{R}{1 - a} = 2 R 1 - a = \frac{1}{2} a = \frac{1}{2} P V^{\frac{1}{2}} = c o n s t a n t d) C = C_{v} - 2 R \frac{R}{1 - a} = 2 R 1 - a = \frac{1}{2} a = \frac{3}{2} P V^{\frac{3}{2}} = c o n s \tan t$

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	Column – I		Column – II
(a)	$P V^{- 2} = c o n s t a n t$	(p)	If volume increases then temperature will also increase
(b)	$P V^{2} = c o n s t a n t$	(q)	If volume increases then temperature will decrease
(C)	$C = C_{v} + 2 R$	(r)	For expansion, heat will have to be supplied to the gas
(d)	$C = C_{v} - 2 R$	(s)	If temperature increases then work done by gas is positive
		(t)	If pressure increases the work done by gas is negative