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. `nR(1 + (2T_(0))/(V_(0)))`
B. `nR(2 + (T_(0))/(V_(0))`
C. `nR(1 + (T_(0))/(V_(0))`
D. `nR(1 + (T_(0))/(2V_(0))`

Answer

C

Explanation

Bulk's modulus `K = (-dp)/(dV//V) = ga,,aP[PV^(gamma)=constant)`
For the curve `TV^(gamma-1)=k` (constant)
or `V dT + T(gamma-1)dV = 0`
or `(dV)/(dT) = (-V)/((gamma-1)T) = -1`
`:. Gamma = 1+(V_0)/(T_0)`
`:. K = gamma[(nRT_0)/(V_0)] = nR(1+(T_0)/(V_0))`.