Question

On a volume-temperature diagram a process $1-2$ is an upward sloping straight line having the tendency to cut the volume axis as shown in the figure ahead. During this process the pressure

• A. Remains constant
• B. continuously increases
• C. continuously decreases
• D. Data insufficient

Answer 1

The correct option is B continuously increases

Given:V-T graph

Solution:

The V-T graph is a straight line with some y-intercept.

Let at point 1 pressure is $P_1$, temperature is $T_1$ and at point 2 $P_2$, temperature is $T_2$

Let the equation of straight line be $V=mT+B$ where $m$ is the slope of the line and $B$ is the y intercept ( both m,B>0).

$PV=nRT$

Putting the value of V in the above equation, we get,

$P=\frac{nRT}{mT+B}$

$\Rightarrow P=\frac{nR}{m+\left(\frac{B}{T}\right)}$

As, $T_2>T_1$

$\Rightarrow \frac{B}{T_1}>\frac{B}{T_2}$

$\therefore P_2>P_1$

So,pressure continously increases.

Hence the correct option is B.