One mole of an ideal gas is contained with in a cylinder by a frictionless piston and is initially a

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11.Thermodynamics

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One mole of an ideal gas is contained with in a cylinder by a frictionless piston and is initially at temperature $T$. The pressure of the gas is kept constant while it is heated and its volume doubles. If $R$ is molar gas constant, the work done by the gas in increasing its volume is

A

$RT\, ln2$

B

$1/2 \,\,RT$

C

$RT$

D

$3/2\,\, RT$

Solution

Expression for work done is given by.

$W=P \Delta V$

Given that

$\mathrm{P}=$ Constant

And volume is doubled from initial position.

$W=P(2 V-V)$

$=P V$

But, by ldeal gas equation $P V=n R T$

For $1$ mole gas, $P V=R T$

$\Rightarrow W=R T$

Standard 11

Physics

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