Figure shows the adiabatic curve for `n` moles of an ideal gas, the bulk modulus for the gas corresponding to the point `P` will be

Options

A. `(5 nRT_(0))/(3 V_(0))`
B. `nR (2 + (T_(0))/(V_(0)))`
C. `nR (1 + (T_(0))/(V_(0)))`
D. `(2 nRT_(0))/(V_(0))`

Answer

D

Explanation

d. For adiabatic process :
Bulk modulus : `B = gamma P`
for point `p : P = (nRT)/(V) = (nR 3 T_(0))/(3 V_(0)) = (nRT_(0))/(V_(0))`
`implies B = (gamma nRT_(0))/(V_(0))`
Now `TV^(gamma - 1) =` constant
`implies (gamma - 1) TdV + VdT = 0`
`implies (dV)/(dT) = (-V)/((gamma - 1) T)`
for point `P rarr`
`(-3 V_(0))/(3 T_(0)) = (- (3 V_(0)))/((gamma -1) (e T_(0))0`
`implies gamma = 2`
so from Eq. (i) `B = (2 nRT_(0))/(V_(0))`