Question

A gas presents in a cylinder,expands against a constant pressure of 1 atm from a volume of 2 litre to a volume of 6 litres. In doing so,it absorbs $800$ joule heat from surrounding. The change in internal energy of process is:

• A. $+305.85$ joule
• B. $+796$ joule
• C. $+396$ joule
• D. $-463.28$ joule

Answer 1

The correct option is C $+396$ joule

Solution:- (C) $+396\text{joule}$

Since work is done against constant pressure, i.e., the process is irreversible.

Given:-

$\Delta V=V_2-V_1$

Given that the gas expands from a volume of $2L$ to the volume of $6L$.

$\therefore \Delta V=6-2=4L$

$\therefore W=-P\Delta V=-1\times 4=-4atm=-405.3J$

From first law of thermodynamics-

$q=\Delta U-W$

$\Rightarrow \Delta U=q+w$

Given that $q=800J$

$\therefore \Delta U=800+(-405.3)=800-405.3=394.7J\approx 396J$

Hence the correct answer is $+396J$.