A cyclinder contains `0.5` mole of an ideal gas at `310K`. As the gas expands isothermally from an initial volume `0.31m^(3)` to a final volume of `0.45m^(3)`, find the amount of heat that must be added to the gas in order to maintain a constant temperature.

Explanation

Here, `n= 0.5 mol e , T= 310K`,
`V_(1)= 0.31m^(3), V_(2)=0.45m^(3), dQ=?`
As the process is isothermal, `dU=0`
`dW= nRT log_(e)((V_(2))/(V_(1)))`
`=0.5xx8.31xx310log_(e)((0.45)/(0.31))`
`dW= 0.5xx8.31xx310xx2.303log_(10)((0.45)/(0.31))`
`dW= 480J`
`dQ=dU+dW=0+480= 480J`
`=(480)/(4.2)cal. = 114cal.`