For a monoatomic ideal gas undergoing an adiabatic change, the relation between temperature and volume is `TV^(x)` = constant, where x is

Options

A. `7//5`
B. `2//5`
C. `2//3`
D. `1//3`

Answer

C

Explanation

For an adiabatic change, `TV^(gamma - 1)` = constant …(i)
`TV^(x)` = constant (Given) ….(ii)
Comparing (i) and (ii), we get `x = gamma - 1`
For a monatomic gas, `gamma = (5)/(3) :. x = (5)/(3) - 1 = (2)/(3)`