Question

Variation of internal energy $\left(U\right)$ with density $\left(\rho \right)$ , of $1mole$ of monatomic gas is depicted in the diagram below. The corresponding variation of pressure with volume can be depicted as: (assume the curve is rectangular hyperbola)

• A.
• B.
• C.
• D.

Answer 1

Answer: (D)

From the equation of rectangular hyperbola and given graph, $U\rho =\text{constant}$
Since the internal energy $U \propto T$ . Therefore, $T\rho =\text{constant}$
Since, the density of ideal gas is $\rho =\frac{M P}{R T}$
$\Rightarrow P=\frac{R \left(T \rho \right)}{M}=\text{constant}$
Here, $P$ is the pressure of the gas which will be constant.
The correct answer will be,