1.

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 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» Correct Answer - D
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))`


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