Question

In a thermodynamic process, pressure of a fixed mass of a gas is changed in such a manner that the gas releases $20\text{J}$ of heat, when $8\text{J}$ of work is done on the gas. If the initial internal energy of the gas was $30\text{J}$, then the final internal energy will be

• A. $+42\text{J}$
• B. $+18\text{J}$
• C. $-18\text{J}$
• D. $-42\text{J}$

Answer 1

The correct option is B $+18\text{J}$

Heat released by gas $\left(\Delta Q\right)=-20\text{J}$
Work done on gas, $\left(\Delta W\right)=-8\text{J}$
[ Here system is gas. Heat released by the system is taken negative & work done on the system is also taken negative]
We know from $1^{st}$ Law of Thermodynamics
$\Delta Q=\Delta U+\Delta W$
$-20\text{J}=\Delta U-8\text{J}$
$\Rightarrow \Delta U=-12\text{J}$
Given,
Initial internal energy of gas $\left(U_{\text{initial}}\right)=30\text{J}$
$\because \Delta U=U_{\text{final}}-U_{\text{initial}}$
we write that, $U_{\text{final}}=U_{\text{initial}}+\Delta U$
$=30+(-12)=+18\text{J}$
Thus, option (b) is the correct answer.