A gas is undergoing an adiabatic process. At a certain stage A, the values of volume and temperature `(V_(0), T_(0))`. From the details given in the graph, find the value of adiabatic constant `gamma`

Options

A. `(V_(0))/(T_(0) tan theta) + 1`
B. `(V_(0) tan theta)/(T_(0) + 1`
C. `(V_(0) tan^(2) theta)/(T_(0)) + 1`
D. `(V_(0))/(T_(0)) + tan theta`

Answer

A

Explanation

We have, for an adiabatic process, in relation wiht temperature and volume
`TV^(gamma-1)` = constant
Differentiating with respect to `T`
`V^(gamma-1).1+T.(gamma-1)V^(gamma-1)=(V_0)/(T_(0)tan theta)`
`gamma = (V_0)/(T_0 tan theta) + 1`.