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The relation between U,P and V for an i...

The relation between U,P and V for an ideal gas in an adiabatic process is given by U = 2 + 3 PV. The gas is

A

monoatomic

B

diatomic

C

polyatomic

D

either monoatomic or diatomic

Text Solution

Verified by Experts

The correct Answer is:
C
For an adiabatic process, dQ= 0
From the first law of thermodynamics, we get
or ` 0- dU + PdV`
From the given equation
`dU = 3 ( PdV + VdP) + PdV`
` or 4P (dV) +3 V (dP) = 0 or 4 (dV)/V) =-3 ((dP)/P)`
On integrating , we get
` "In"(V^(4) + "In"(P^(3))= "constant or " PV^(4//3)` = constant Compare it with standard equation of an adiabatic process
` PV^(y) ` = constant, we get ` gamma = 4/3 ` i.e, gas is polyatomic .
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