An ideal monatomic gas of mass M is taken through a cyclic process A B C. The process A B is P ρ= constant. Total work done by the gas in the process is -(α/β) M (P0/ρ0). Find (α+β)

Question

An ideal monatomic gas of mass M is taken through a cyclic process A B C. The process A B is P ρ= constant. Total work done by the gas in the process is -(α/β) M (P0/ρ0). Find (α+β) (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

WB arrow C =ρ0(Vf-Vi) =P0((M/ρ0)-(M/3 ρ0))=(2/3) (P0/ρ0) M WA arrow C =0 W text Total =(-4/3) (P0/ρ0) M+(2/3) (P0/ρ0) M =(-2/3) (P0/ρ0) M

Q. An ideal monatomic gas of mass $M$ is taken through a cyclic process $A BC$ . The process $A B$ is $Pρ =$ constant. Total work done by the gas in the process is $- \frac{α}{β} M \frac{P _{0}}{ρ _{0}}$ . Find $(α + β)$

$W_{B \to C} = ρ_{0} (V_{f} - V_{i})$
$= P_{0} (\frac{M}{ρ _{0}} - \frac{M}{3 ρ _{0}}) = \frac{2}{3} \frac{P _{0}}{ρ _{0}} M$
$W_{A \to C} = 0$
$W_{Total} = \frac{- 4}{3} \frac{P _{0}}{ρ _{0}} M + \frac{2}{3} \frac{P _{0}}{ρ _{0}} M$
$= \frac{- 2}{3} \frac{P _{0}}{ρ _{0}} M$

Q. An ideal monatomic gas of mass M is taken through a cyclic process ABC. The process AB is Pρ= constant. Total work done by the gas in the process is −βα​Mρ0​P0​​. Find (α+β)

WB→C​=ρ0​(Vf​−Vi​) =P0​(ρ0​M​−3ρ0​M​)=32​ρ0​P0​​M WA→C​=0 WTotal ​=3−4​ρ0​P0​​M+32​ρ0​P0​​M =3−2​ρ0​P0​​M

Q. An ideal monatomic gas of mass $M$ is taken through a cyclic process $A BC$ . The process $A B$ is $Pρ =$ constant. Total work done by the gas in the process is $- \frac{α}{β} M \frac{P _{0}}{ρ _{0}}$ . Find $(α + β)$

$W_{B \to C} = ρ_{0} (V_{f} - V_{i})$
$= P_{0} (\frac{M}{ρ _{0}} - \frac{M}{3 ρ _{0}}) = \frac{2}{3} \frac{P _{0}}{ρ _{0}} M$
$W_{A \to C} = 0$
$W_{Total} = \frac{- 4}{3} \frac{P _{0}}{ρ _{0}} M + \frac{2}{3} \frac{P _{0}}{ρ _{0}} M$
$= \frac{- 2}{3} \frac{P _{0}}{ρ _{0}} M$