Question

The process $CD$ is shown in the diagram. As system is taken from $C$ to $D$, what happens to the temperature of the system?

• A. Temperature first decreases and then increases
• B. Temperatures first increases and then decreases
• C. Temperature decreases continuously
• D. Temperature increases continuously

Answer 1

The correct option is A Temperature first decreases and then increases

Solution:- (A) temperature first decreases and then increases

From ideal gas equation,

$PV=nRT$

$\Rightarrow T=\frac{PV}{nR}$

Let $P$ be the mid point on $CD$.

At point C-

$P=3p_0$

$V=v_0$

$\therefore T_C=\frac{3p_0{v}_0}{nR}.....\left(1\right)$

At mid-point P-

$P=\frac{p_0+3p_0}{2}=2p_0$

$V=\frac{v_0+3v_0}{2}=2v_0$

$\therefore T_P=\frac{4p_0{v}_0}{nR}.....\left(2\right)$

At point D-

$P=p_0$

$V=3v_0$

$\therefore T_D=\frac{3p_0{v}_0}{nR}.....\left(3\right)$

Now from ${eq}^n\left(1\right),\left(2\right)\&\left(3\right)$, we have

$T_C<T_P>T_D$

Hence the temperature will first decreases and then increases.