Figure shows an isochore, an isotherm, an adiabatic and two isobars of two gases on a work done versus heat supplied curve. The initial states of both gases are the same and the scales for the two axes are same.

Options

A. Straight line 1 corresponds to an isochoric process.
B. Straight line 2 corresponds to an isobaric process for diatomic gas.
C. Straight line 4 corresponds to an isothermal process.
D. Straight line 5 corresponds to an isothermal process.

Answer

D

Explanation

d. From the first law of thermodynamics
`Q = W + Delta U`
For an isobaric process
`W = R Delta T, Q = C_(P) Delta T = ((f + 2)/(2)) R Delta T`
`(W)/(Q) = (2)/(f + 2)`
where f is the number of degrees of freedom For an isochoric process.
`W = 0, (W)/(Q) = 0`
The straight line 1 corresponds toan isochoric process.
For monatoic gas `f = 3` and for diatomic gas `f = 5`.
`(W)/(Q) = (2)/(5)` (for monatomic gas)
`= (2)/(7)` (for diatomic gas)
Straight line 2 corresponds to isobaric process for diatomic gas straight line 3 corresponds to isobaric process for monatomic gas.
For isotherm `W = Q, tan theta_(4) = 1` straight line 4 only if `Delta T = 0` i.e., `Delta U = 0`, For an adiabatic process `Q = 0`, the straight line 5 corresponds to it.