One mole of an ideal gas is kept enclosed under a light piston (area `= 10^(-2)m^(2))` connected by a compressed spring (spring constant `100N//m)`. The volume of gas is `0.83 m^(3)` and its temperature is `100K`. The gas is heated so that it compresses the spring further by `0.1 m`. The work done by the gas in the process is `N xx 10^(-1)J`. Find `N`. (Take `R = 8.3 J//K-"mole")` and suppose there is no atmosphere).

Options

A. `3J`
B. `6J`
C. `9J`
D. `1.5J`

Explanation

Before heating let the pressure of gas be `P_(1)` from the equilibrium piston,
`PA=kx_(1)`
`therefore x_(1)=(PA)/(K)=((nRT)/(V))(A)/(K)=(1xx8.3xx100xx10^(-2))/(0.83xx100)=10^(-1)=0.1m`
Since during heating process.
The spring is compressed further by `0.1m`
`therefore x_(2)=0.2m`
work done by gas `=(1)/(2)100(0.2^(2)-0.1^(2))=(1)/(2)100(0.1)(0.3)=1.50=1.5J`
`=(4piq^(2))/(sqrt(3l))`