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Question:

The variation of volume V, with the temperature T, keeping pressure constant is called the coefficient of thermal expansion (α) of a gas i.e., α = (1/V)(∂V/∂T)P. For an ideal gas α is equal to:

T

1/T

P

1/P

Solution:

For n moles of an ideal gas PV = nRT or V = nRT/P. Differentiating with respect to T at constant P, we have (∂V/∂T)P = nR/P = V/T. α = (1/V) × (V/T) = 1/T. Option B is correct.