A U- U- internal energy of the gas and - density of the gas plot of an ideal mono-atomic gas undergoing a cyclic process is shown in the figure- A-B is part of a rectangular hyperbola- Then which of the following graphs in the options below corresponds to the process given in the adjacent diagram-

For process AB→ U×ρ= constant nC_vT×PMRT= constant ⇒ P= constant Isobaric process. For process BC→ ρ= constant PMRT= constant P∝T Isochoric process. For ...

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Standard XII

Physics

Work Done

A U-ρ U→ inte...

Question

A $U - ρ (U \to$ internal energy of the gas and $ρ \to$ density of the gas) plot of an ideal mono-atomic gas undergoing a cyclic process is shown in the figure. $A \to B$ is part of a rectangular hyperbola. Then which of the following graphs in the options below corresponds to the process given in the adjacent diagram?

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Solution

The correct option is C
For process $AB \to$
$U \times ρ =$ constant

${nC}_{v} T \times \frac{PM}{RT} =$ constant

$\Rightarrow P =$ constant

Isobaric process.

For process $BC \to$
$ρ =$ constant

$\frac{PM}{RT} =$ constant

$P \propto T$

Isochoric process.

For process $CA \to$
$U =$ constant

$U = {nC}_{v} T =$ constant

$T =$ constant

Isothermal process

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The correct option is C For process AB→ U×ρ= constant nCvT×PMRT= constant ⇒P= constant Isobaric process. For process BC→ ρ= constant PMRT= constant P∝T Isochoric process. For process CA→ U= constant U=nCvT= constant T= constant Isothermal process