Question

When 100 J of heat is given to an ideal gas it expands from 200 $c{m}^3$ to 400 $c{m}^3$ at a constant pressure of $3\times {10}^5$ Pa. Then calculate the change in internal energy of the gas :

$R=[\frac{25}{3}J/mol-k]$

• A. 10 J
• B. 40 J
• C. 30 J
• D. None of these

Answer 1

The correct option is B 40 J

$\Delta U=\Delta Q-W$ where $\Delta U$ is the change in internal energy, $\Delta Q$ is the heat supplied to the system and $W$ is the work done by the syatem.
Given: $\Delta Q=100J$
$W={\int }_{200}^{400}Pdv={\int }_{200}^{400}3\times {10}^{5}dv=3\times {10}^5\times (400-200)\times {10}^{-6}=60J$
$\Delta U=\Delta Q-W=(100-60)=40J$