Question

A gas expands such that its initial and final temperature are equal. Also, the process followed by the gas traces a straight line on the P-V diagram:

• A. The temperature of the gas remains constant throughout
• B. The temperature of the gas first increases and then decreases
• C. The temperature of the gas first decreases and then increases
• D. The straight line has negative slope

Answer 1

Answer: (B), (D)

The correct options are
B The temperature of the gas first increases and then decreases
D The straight line has negative slope

The straight line in P-V graph P= mV + c, can have slope m>0, m=0 or m<0
For m=0, P=c $\Rightarrow$ increase in volume implies increase in temperature
For m>0, P and V both increase and decrease simultaneouly$\Rightarrow$ increase in V accompanies increase in PV which in turn means increase in T.
For m<0, applying ideal gas equation $PV=nRT\Rightarrow dP/P+dV/V=dT/T\Rightarrow mdV/(mV+c)+dV/V=dT/T\Rightarrow dT/dV=T(\frac{1}{V+c/m}+\frac{1}{V})$
m<0$\Rightarrow$ c/m<0 $\Rightarrow$ dT/dV>0 for small V(<-c/2m) but <0 for large V(>-c/2m)
Hence temperature first increases and then decreases
So, b and d are correct options