Question

Figure shows graphs of pressure vs density for an ideal gas at two temperatures $T_{1}$ and $T_{2} .$ Which of the following is correct?

• A. $T_{1} >T_{2}$
• B. $T_{1} =T_{2}$
• C. $T_{1} < T_{2}$
• D. any of the three is possible.

Answer 1

Answer: (A)

$P=\left(\frac{\rho}{M}\right) R T$
$ \Rightarrow P=\left(\frac{R T}{M}\right) \rho$
Comparing with $y=m x$
Slope $=\frac{R T}{M}$ or slope $\propto T$
Since $T_{1}$ has a greater slope than
$T_{2} \Rightarrow T_{1}>T_{2}$