Question

During an adiabatic expansion of 2 moles of a gas, the change in internal energy was found to be equal to $-200J$. The work done during the process will be equal to
A. $-100J$
B. $0J$
C. $100J$
D. $200J$

Answer 1

An adiabatic process is a thermodynamic process in which the change in heat energy of the gas is zero. Use the first law of thermodynamics and find the relation between change in internal energy and work done by a gas in an adiabatic process.

Formula used:
$\Delta Q=W+\Delta U$

Complete step by step answer:
Let us first understand what an adiabatic process is.

An adiabatic process is a thermodynamic process in which the change in heat energy of the gas is zero. This means that neither the gas takes in energy nor it gives out energy.
When a gas absorbs some amount of energy, there is a change in the internal energy of the gas and the gas does some work.

From the first law of thermodynamics we know that $\Delta Q=W+\Delta U$ …. (i),
where $\Delta Q$ is the energy absorbed or dissipated by the gas, W is the amount of work done by the gas and $\Delta U$ is the change in internal energy of the gas.
However, in an adiabatic process, neither the gas takes in energy nor it gives out energy. This means that in an adiabatic process, $\Delta Q=0$.

Substitute this value in (i).
$\Rightarrow W+\Delta U=0$
$\Rightarrow W=-\Delta U$ …. (ii)

This means that during an adiabatic process, the work done by the gas is equal to the negative of the change in its internal energy.

It is given that the change in internal energy of the gas is -200J. Therefore, $\Delta U=-200J$.

Substitute this value in (ii).
$\Rightarrow W=-(-200J)=+200J$.

Therefore, the work done by the gas in this process is equal to 200J.

Hence, the correct option is D.

Note: Internal energy is the total energy possessed by the molecules of the gas in the form of translational kinetic energy and rotational kinetic energy.
Note that we cannot measure the absolute value of internal energy. However, we can measure the change in internal energy of gas.
Change in internal energy of a gas is a path independent function. Whereas work done is a path dependent function.