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During an experiment, an ideal gas is found to obey a condition $P^{2} / ρ$ = constant ( $ρ$ = density of the gas). The gas is initially at temperature T, pressure P and density $ρ$ . The gas expands such that density changes to $ρ$ /2.

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The pressure of the gas changes to 2P.

The temperature of the gas changes to 2T.

The graph of the above process on the P-T diagram is parabola.

The graph of the above process on the P-T diagram is hyperbola.

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detailed solution

Correct option is B

P2ρ=k ⇒ P2RTPM=kPT=kMR⇒P∝1T ...(i)P2ρ=P′2ρ/2 ⇒ P′=P2Hence, from Eq. (i) T′=T2PT = constant, hence P-T curve is a parabola.

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During an experiment, an ideal gas is found to obey a condition P2/ρ = constant (ρ = density of the gas). The gas is initially at temperature T, pressure P and density ρ. The gas expands such that density changes to ρ/2.

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Ready to Test Your Skills?

free study material

During an experiment, an ideal gas is found to obey a condition $P^{2} / ρ$ = constant ( $ρ$ = density of the gas). The gas is initially at temperature T, pressure P and density $ρ$ . The gas expands such that density changes to $ρ$ /2.