A process in which work perfomed by an ideal gas is proportional to the corresponding increment of its internal energy is described as a polytropic process. If we represent work done by a ppolytropic process by `W` and increase in internal energy as `Delta U` then
`W prop Delta U`
or `W=K_(1) DeltaU` ...(i)
For this process, it can be demonstrated that the relation between pressure and volume is given by the equation
`PV^( eta)= K_(2)` (constant ) .....(ii)
We know that a gas can have various values for molar specific heats. The molar specific heat `'C'` for an ideal gas in polytropic process can be calculated with the help of first law of thermodynamics. In polytropic process process the variation of molar specific heat `'C'` with `eta` for a monatomic gas is plotted as in the graph shown.

In the graph shown, the `y-` coordinate of point `A` is ( for monatomic gas )

Options

A. `1 lt eta lt (2)/(3)`
B. `1 lt eta lt (8)/(3)`
C. `1 lt eta lt (5)/(3)`
D. `(2)/(3) lt eta lt (8)/(3)`

Answer

C

Explanation

`C rarr +- alpha`
is negative for `1 lt eta lt gamma`