Question

In a thermodynamic process pressure of a fixed mass of a gas is changed in such a manner that the gas releases $30\, J$ of heat and $10\, J$ of work was done on the gas. If the initial internal energy of the gas was $30\, J$, then the final internal energy will be

• A. 2 J
• B. -18 J
• C. 10 J
• D. 58 J

Answer 1

Answer: (C)

Given, heat, $Q=-30\, J$
Work done on the gas, $W=-10\, J$
Initial internal energy, $U_{i}=-10\, J$
Final internal energy, $U_{f}=?$
According to first law of thermodynamics,
$Q=W+\Delta U$
$\Rightarrow -30=-10+U_{i}-U_{f}$
$\Rightarrow -30=-10-10-U_{f}$
$\Rightarrow 30=10+10+U_{f}$
$\Rightarrow 30-20=U_{f}$
$\Rightarrow U_{f}=10\, J$