Question

A motor draws some gas from an adiabatic container of volume 2 liters having a monatomic gas at a pressure 4 atm. After drawing the gas the pressure in the container reduces to 1 atm. If the motor converts 10% of the energy contained in the drawn gas and the output of the motor is 10p joule, then p is
( Use $1atm={10}^{5}pascal)$

• A. 9
• B. 4
• C. 8
• D. 6

Answer 1

The correct option is A 9

We have internal energy of a gas in a container,

$U=\frac{f}{2}nRT$

$=\frac{f}{2}PV$ (as $PV=nRT$)

$=\frac{3}{2}PV$ (as $f=3$ for a monoatomic gas)

The initial internal energy is given by

$U_i=\frac{3}{2}\times 4\times 2=12atm-litre$

The final internal energy is given by

$U_f=\frac{3}{2}\times 1\times 2=3atm-litre$

Total energy of the gas drawn $=9atm-litre=911.7J$ ($1atm-litre=101.3J$)

Output of the motor = 10 % of 911.7 = 91.2 J ~ 90 J =10 p

Hence $p=9$