Draw the approximate plots of isochoric, isobaric, isothermal, and adiabatic processes for the case of an ideal gas, using the following variables :
(a) `p, T `:
(b) `V , T`.

Explanation

(a) From ideal gas law `p = ((vR)/(V)) T = kT(where k = (vR)/(V))`
For isochoric process, obviously `k = constant`, thus `p = kT`, represents a staight line passing through the origin and it slope becomes `k`.
For isobaric process `p = constant`, thus on `p - T` curve, it is a horizontal straight line parallel to `T - axis` if `t` is along horizontal (or `x - axis`)
For adiabatic process `T^gamma P^(1 - gamma) = constant`
After differentiating, we get `(1 - gamma)p^(- gamma) dp.T^gamma + gamma p^(1 - gamma).dT = 0`
`(dp)/(dT) = ((gamma)/(1 - gamma)) (p^(1 - gamma))/(p^(- gamma)) (T^(gamma -1)/(T^gamma)) = ((gamma)/(gamma - 1)) (p)/(T)`
The approximate plots of isochoric, isobaric, isothermal, and adiabatic processess are drawn in the answeresheet.
(b) As `p` is not considered as variable, we have fromm ideal gas law
`V = (vR)/(p) T = k' T(where k' = (v R)/(p))`
On `V - T` co-ordinate system let us, take `T` along `x - axis`.
For isochoric process `V = constant`, thus `k = constant` and `V = k'T` obviously represents a staight line passing through the origin of the co-ordinate system and `k` is its slope.
For isothermal process `T = constant`. Thus on the stated co-ordinate system it represents a straight line parallel to the `V - axis`.
For adiabatic process `TV^(gamma - 1) = constant`
After differentiating, we get `(gamma - 1)V^(gamma - 2) dV. T + V^(gamma - 1) dT = 0`
`(dV)/(dT) = -((1)/(gamma - 1)).(V)/(T)`
The approximate plots of isochoric, isobaric, isothermal and adiabatic process are drawn in the answer sheet.