Variation of internal energy (U) with density (ρ ) , 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)

Question

Variation of internal energy (U) with density (ρ ) , 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) Question

(A)

(B)

(C)

(D)

Tardigrade Admin · Accepted Answer

From the equation of rectangular hyperbola and given graph,

U ρ = constant

Since the internal energy

U \propto T

. Therefore,

Tρ = constant

Since, the density of ideal gas is

ρ = \frac{MP}{RT}

\Rightarrow P = \frac{R ( Tρ )}{M} = constant

Here,

P

is the pressure of the gas which will be constant.
The correct answer will be,
Solution

Q. Variation of internal energy (U) with density (ρ) , 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)

From the equation of rectangular hyperbola and given graph, Uρ=constant Since the internal energy U∝T . Therefore, Tρ=constant Since, the density of ideal gas is ρ=RTMP​ ⇒P=MR(Tρ)​=constant Here, P is the pressure of the gas which will be constant. The correct answer will be,

Q. Variation of internal energy $(U)$ with density $(ρ)$ , of $1 m o l e$ 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)