# A gas is made to expand in such a way that its final and initial temperatures are equal and also the process followed by the gas traces a straight line of the PV diagram. Then, which of the following statements is true?

(A) the temperature of the gas remains constant throughout the process (B) the temperature of the gas first increases and then decreases during the process (C) the temperature of the gas first decreases and then increases during the process (D) None of the above

Since the graph has a straight line, it can have either a positive or negative slope. But a positive slope means an ever increasing product of PV, so it has to have a negative slope only, which looks like this:
Since $PV = nRT$ and $P = kV + C$ (from the graph, where $k \gt 0$, we have:
$T = \large\frac{V (-kV + C)}{nR}$
So, T varies with V as shown below. Hence, (B) (the temperature of the gas first increases and then decreases during the process) is the correct option
edited Mar 23, 2014