Question

One mole of an ideal gas is contained within 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. $\frac{RT}{2n}$
• B. $\frac{1}{2}RT$
• C. RT
• D. $\frac{3}{2T}$

Answer 1

Answer: (C)

RT

Expression for work done is given by,

$W=P\Delta V$

Given that

P= Constant

And volume is doubled from initial position.

$W=P(2V-V)$

$=PV$

But, by Ideal gas equation $PV=nRT$

For 1 mole gas, $PV=RT$

$=2RT-RT=RT$.

$\Rightarrow W=RT$

Hence, the correct option is $C$