Question

A gas present in a cylinder fitted with a frictionless piston expands against a constant pressure of $1$ atm from a volume of $2$ litre of the volume of $6$ litre. In doing so, it absorbs $800$ J heat from surroundings. The increase in internal energy of the process is

• A. $394.95J$
• B. $395.96J$
• C. $392.95J$
• D. $391.96J$

Answer 1

The correct option is A $394.95J$

The work is done against constant pressure. Hence, the expansion is irreversible.
The change in volume is $\Delta V=(6-2)=4L$. The pressure is $P=1$.
The work done is $W=-P\times |DeltaV|=1\times 4=-4litreatm$
Convert the work from litre atm to cal and then to J.
$\frac{1\times 4\times 1.987}{0.0821}cal=-96.81=-96.81\times 4.184J=-405.05J$.
By applying first law of thermodynamics,
$q=\Delta U-W$
Substitute values in the above expression:
$800=\Delta U+405.05$
Hence, $\Delta U=394.95J$