JEE Main · 2024 · 08 Apr 2024 · Shift 1 · Heat & Thermodynamics

Two different adiabatic paths for the same gas intersect two isothermal curves as shown in P-V diagram. The relation between the ratio

\frac{V _{a}}{V _{d}}

and the ratio

\frac{V _{b}}{V _{c}}

is:

Answer: (C)

Solution

For an adiabatic,

T V^{γ - 1} = const

. Along a–d:

T_{a} V_{a}^{γ - 1} = T_{d} V_{d}^{γ - 1}

; along b–c:

T_{b} V_{b}^{γ - 1} = T_{c} V_{c}^{γ - 1}

. From the diagram a,b lie on one isotherm (

T_{a} = T_{b}

) and c,d on the other (

T_{c} = T_{d}

). Dividing the two relations gives

(\frac{V _{a}}{V _{d}})^{γ - 1} = (\frac{V _{b}}{V _{c}})^{γ - 1}

, hence

\frac{V _{a}}{V _{d}} = \frac{V _{b}}{V _{c}}

. Option (C).

JEE Main · 2024 · 08 Apr 2024 · Shift 1 · Single correct option