Figure. Shows the `P-V` diagram for a Carnot cycle. In this diagram

Options

A. curve `AB` represents isothemal process and `BC` adiabatic process
B. curve `AB` represents adiabatic process and `BC` isothermal process
C. curve `CD` represents isothermal process and `DA` adaibatic process
D. curve `CD` represent adiabatic process and `DA` isothermal process

Answer

A, C

Explanation

For an adiabatic process, `PV^( gamma)=` constant . Differentiating w.r.t. `V`, we get
`(d P)/( dV) V^( gamma)+ P gammaV^( gamma-1)=0`
or ` ( dP)/( dV) =-( gamma P)/(V)`
For isothermal process, `PV=` constant.
Hence,
`(dP)/( dV) =-(P)/(V)`
Now, `dP//dV` is the slope of the `(P-V)` graph. Thus, the slope of the `( P-V)` graph for an adiabatic process is `gamma` times that for an isothermal process. Hence, curves `BC` and `DA` both represent adaibatic process and curves `AB` and `CD` both represent isothermal process. Thus, the correct choices are `(a)` and `(c)`.