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.

60 mins Expert Faculty Ask Questions

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.

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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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?

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