First slide

Thermal expansion

Question

A gas obeys ${PV}^{2}$ =constant in addition to PV=RT. If on heating, the temperature is doubled. The volume of the gas is

Moderate

A

$\frac{V}{2}$
B

$2 V$
C

$V / \sqrt{2}$
D

$\sqrt{2} V$

Solution

given ${PV}^{2} =$ constant-----(1)
here P is pressure; V is volume; R is universal gas constant; T is temperature of gas
$also given PV=RT \Rightarrow P= \frac{RT}{V} ---(2)$
substitute eqn(2) in eqn(1)
$⇒ \frac{R T}{V} V^{2} =constant \Rightarrow T V = c o n s \tan t b e c a u s e R i s c o n s t a n t$
$T α \frac{1}{V} f o r t w o d i f f e r e n t t e m p e r a t u r e s o f s a m e g a s \frac{T_{1}}{T_{2}} = \frac{V_{2}}{V_{1}} g i v e n T_{1} = T; T_{2} = 2 T; l e t V_{1} = V s u b s t i t u t e i n a b o v e e q u a t i o n V_{2} = \frac{V}{2} = f i n a l v o l u m e o f g a s$

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