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Question

# During an experiment, an ideal gas is found to obey a condition P2ρ =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 ρ2

A
The pressure of the gas changes to 2P
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B
The temperature of the gas changes to 2T
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C
The graph of the above process on the P-T diagram is parabola.
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D
The graph of the above process on the P-T diagram is hyperbola.
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Solution

## The correct options are B The temperature of the gas changes to √2T D The graph of the above process on the P-T diagram is hyperbola.Equation of process ⇒P2ρ= constant =C .... (1)Equation of state ⇒Pρ=RMT .... (2)From 1 and 2,PT= constant ⇒ C is false, D is true.Now, ρ-changes to ρ2⇒ P changes to P√2 from equation (1)⇒ A is false.Hence, T changes to √2T⇒ B is true

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