An ideal gas of n moles is taken from state 1 to state 2. On a...

According to the ideal gas equation, $PV = nRT$, which can be rearranged as $P = \left(\dfrac{nR}{V}\right)T$.

The process is given as a straight line passing through the origin on the $P-T$ diagram. The equation of such a line is $P = kT$, where $k$ is a constant slope.

Comparing the two equations, we get $\dfrac{nR}{V} = k$. Since $n$, $R$, and $k$ are constants, the volume $V$ must also be constant.

A process where the volume remains constant is an isochoric process ($\Delta V = 0$).

The work done by a gas is given by $W = \int P \, dV$. Since there is no change in volume, the work done by the gas is zero.

Answer: Zero