The equation of state for a gas is given by `PV = eta RT + alpha V`, where `eta` is the number of moles and `alpha` a positive constant. The intinal pressure and temperature of 1 mol of the gas contained in a cylinder is `P_(0)` and `T_(0)`, respectively. The work done by the gas when its temperature doubles isobarically will be

Options

A. `(P_(0) T_(0) R)/(P_(0) - alpha)`
B. `(P_(0) T_(0) R)/(P_(0) + alpha)`
C. `P_(0) T_(0) R` 1n 2
D. none of these

Answer

A

Explanation

a. `Delta W = P Delta V`, given , `PV = mu RT + alpha V`
`:. P Delta V = mu R Delta T + alpha Delta V`
or, `Delta V = [(mu R Delta T)//(P_(0) - alpha)]`
i.e., `Delta W = (P_(0) RT_(0))/(P_(0 - alpha) (mu - 1)`