For an adiabatic change the value of `(dP)/(P)` is equal to `(dV=" change in vol.," gamma =(C_(p))/(C_(v)))`:

Options

A. `gamma^(1//2) cdot (dV)/(V)`
B. `-(dV)/(V)`
C. `-gamma cdot (dV)/(V)`
D. `-gamma^(2)(dV)/(V)`

Answer

C

Explanation

Here `(d)/(dP) (P. V^(gamma)) =(d)/(dP)` (constant)
or `V^(gamma) +gamma V^(gamma-1)P(dV)/(dP)=0`
or `V^(gamma) =-gamma V^(gamma-1)P. (dV)/(dP)`
or `(dP)/(P) =(-gamma V^(gamma-1))/(V^(gamma)). dV =-gamma. (dV)/(V).`
`therefore` Correct choice is (c ).