Question

The volume of gas decreases from $500cc$ to $300cc$ when a sample of gas is compressed by an average pressure of $0.6atm$. During this process, $10J$ of heat is liberated. The change in internal energy is:

• A. $-2.16J$
• B. $12.156J$
• C. $2.16J$
• D. $101.3J$

Answer 1

The correct option is C $2.16J$

Solution:- (C) $2.16J$

As the heat is liberated,

$\therefore q=-10J$

Now, as we know that the work done is given as-

$W=-P_{ext.}\Delta V$

Given:-

$P_{ext.}=0.6atm$

$V_1=500cc$

$V_2=300cc$

$\Rightarrow \Delta V=300-500=-200cc=-0.2L$

$\therefore W=-0.6\times (-0.2)=0.12L-atm=12.16J$

Now, from first law of thermodynamics,

$\Delta U=q+W$

$\Rightarrow \Delta U=-10+12.16=2.16J$

Hence the change in internal energy is $2.16J$.