Questions

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

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a
The pressure of the gas changes to 2P.
b
The temperature of the gas changes to 2T.
c
The graph of the above process on the P-T diagram is parabola.
d
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.

One mole of an ideal monoatomic gas is taken through process AB given by $\mathrm{P}=\mathrm{\alpha }-{\mathrm{\beta V}}^{2}$ (where $\mathrm{\alpha }$ and $\mathrm{\beta }$ are positive constants) on P-V diagram. Which of the following is the correct statement regarding the given process?