Question

Two different adiabatic parts for the same gas intersect two isothermals at T1 and T2 as shown in P-V diagram. Then the ratio of $\frac { V _ { a } } { V _ { b } }$ will be

• A. $\frac { V _ { c } } { V _ { d } }$
• B.
• C. $\gamma$
• D.

Answer 1

Answer: (B)

Answer 2

: For adiabatic curve BC

$T _ { 1 } V _ { b } ^ { \gamma - 1 } = T _ { 2 } V _ { c } ^ { \gamma - 1 }$ ….. (i)

Again for adiabatic curve AD

$T _ { 1 } V _ { a } ^ { \gamma - 1 } = T _ { 2 } V _ { d } ^ { \gamma - 1 }$….. (ii)

Dividing (i) by (ii)

$\left( \frac { V _ { b } } { V _ { a } } \right) ^ { \gamma - 1 } = \left( \frac { V _ { c } } { V _ { d } } \right) ^ { \gamma - 1 }$

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