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Question

# The equation of state of a gas is (P+aT2V)×Vc1=(RT+b) where a, b, c and R are constants. The isotherms can be represented by P=AVm−BVn where A and B depend only on temperature. Then,

A

m = - c, n = -1

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B

m = c, n = 1

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C

m = -c, n = 1

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D

m = c, n = -1

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Solution

## The correct option is A m = - c, n = -1 Expanding the equation of state we have PVc+aT2 Vc−1=RT+bor P=−aT2 V−1+RT V−c+bV−cor P=AV−c−BV−1 .....(i)where A=RT+b and B=aT2. We are given that P=A Vm−BVn .......(ii) Comparing the power of V in (i) and (ii) we get m = -c and n = -1.

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