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. `3R//2`
B. `5R//2`
C. `7R//2`
D. `4R`

Answer

B

Explanation

For point `A, eta=0`
`:. C=( R(0-gamma))/((0-1)(gamma-1))=(gammaR)/(gamma-1)=(5)/( 2) R`