Question

The internal energy of a gas is given by $U=(2PV+20)\text{J}$. It expands from $100{\text{cm}}^3$ to $200{\text{cm}}^3$ against a constant pressure of $200\text{kPa}$. Calculate the heat absorbed by the gas in the process.

• A. $-60\text{J}$
• B. $40\text{J}$
• C. $-40\text{J}$
• D. $60\text{J}$

Answer 1

The correct option is D $60\text{J}$

At we know,
$Q=\Delta U+W$
Given, $U=2PV+20$
$\Rightarrow \Delta U=2P\Delta V$ [$P$ is constant]
$=2\times 200\times {10}^3\times (200-100)\times {10}^{-6}$
$=4\times {10}^5\times 100\times {10}^{-6}$
$=40\text{J}$
$W=P\Delta V$
$=200\times {10}^3\times (200-100)\times {10}^{-6}$
$=20\text{J}$
So, $Q=\Delta U+W=40+20=60\text{J}$
Heat absorbed by the gas is $60\text{J}$.