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Heat and Thermodynamics question

2016 · 10 Apr · Shift 1 · Q44

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Heat and Thermodynamics
2016 · 10 Apr · Shift 1 · Q44

Heat and Thermodynamics question

2016 · 10 Apr · Shift 1 · Q44

JEE MainPhysicsHeat and ThermodynamicsMCQ+4 / −1

Which of the following shows the correct relationship between the pressure ‘P’ and density

\rho

of an ideal gas at constant temperature ?

A
B
C
D

View written solutionFree

Correct answer: D

For an ideal gas, the equation of state is

$PV=nRT$

Write density in terms of mass and volume:

$\rho=\frac{m}{V}$

Also, number of moles

$n=\frac{m}{M}$

where $M$ is the molar mass.

Substitute $n=\frac{m}{M}$ into the ideal gas equation:

$PV=\frac{m}{M}RT$

Rearranging,

$P=\frac{m}{V}\cdot \frac{RT}{M}$

Since

$\frac{m}{V}=\rho$

we get

$P=\rho\frac{RT}{M}$

At constant temperature $T$ , and for a given gas $M$ is constant, so

$P\propto \rho$

Thus, pressure is directly proportional to density. The correct graph/relationship is a straight line passing through the origin.

Therefore, the correct option is the one representing

$P \propto \rho$

Given the stored correct answer is D, this matches the derived result.

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