Question

Volume versus temperature graphs for a given mass of an ideal gas are shown in figure. At two different values of constant pressure. What can be inferred about relation between $p_1$ and $P_2$ ?

• A. $p_1>p_2$
• B. $p_1=p_2$
• C. $p_1<p_2$
• D. data is insufficient

Answer 1

Answer: (A)

$pV=nRT\Rightarrow V=\left(\frac{nR}{p}\right)T$ Slope of the $V-T$ graph, $m=\frac{dV}{dT}=\frac{nR}{p}$ $\Rightarrow$ $m\propto \frac{1}{p}$ [ $\therefore$ $nR=$ constant] Or $p\propto \frac{1}{m}$ Hence, $\frac{p_2}{p_1}=\frac{m_1}{m_2}<1$ where, $m_1$ is slope of the graph corresponding of $p_1$ and similarly $m_2$ is slope corresponding to $\Rightarrow$ $p_2<p_{1}or{p}_1>p_2$