Question

During the adiabatic expansion of $2$ moles of a gas, the internal energy of the gas is found to decrease by $2$ joules, the work done during the process on the gas will be equal to

• A. $1J$
• B. $-1J$
• C. $2J$
• D. $-2J$

Answer 1

The correct option is D

$-2J$

Step 1: Given:

Change in internal energy, $∆U=-2J$

Step 2: Formula used:

$∆Q=∆U+∆W$, where $∆Q$ is the change in the heat of the system, $∆U$ is the change in internal energy, and $∆W$ is the work done.

Step 3: Calculating work done

We know that for adiabatic expansions, $∆Q=0$,

So,

$$\begin{gathered} ∆Q+∆W=0 \\ ∆W=-∆U \\ ∆W=-\left(-2\right) \\ ∆W=2J \end{gathered}$$

This is the work done by the gas.

Thus, the work done on the gas will be $-2J$.

So, option D is the correct answer.