Question

The volume $\left(V\right)$ versus temperature $\left(T\right)$ graph of an ideal gas of given mass, undergoing a thermodynamic process is shown below. During this process, if the temperature increases, then the pressure of the gas

• A. first increases then decreases
• B. continuously decreases
• C. continuously increases
• D. first decreases then increases

Answer 1

The correct option is B continuously decreases

By Extrapolating the given graph we get,
$V=mT-c..........\left(1\right)$
Here, $m$ is the slope of straight line and $c$ is the negative $y-$ intercept.

From the ideal gas equation,
$PV=nRT$
we can write that,
$P=\frac{nRT}{V}$
$\Rightarrow P=\frac{nRT}{mT-c}$ [from (1)]
$\Rightarrow P=\frac{nR}{m-\frac{c}{T}}$
From this, we can see that, as $T$ increases, $\frac{c}{T}$ decreases, $(m-\frac{c}{T})$ increases, hence, $P$ decreases.
Therefore, pressure decreases continuously as temperature increases continuously in the given thermodynamic process.
Thus, option (b) is the correct answer.