What will be the final volume of a mole of an idela gas at `20^(@)C` when it expands adiabatically from a volume of `5L` at `30^(@)C? C_(V)` of the gas `=5 cal//degree`.

Explanation

Given,
`n = 1, T_(2) = (273 +20) = 293 K, V_(1) = 5L, V_(2) = ?, T_(1) = 303K`
From the first law,
`dq +dw = dU`
`dq = 0` (adiabatic process)
or `dU =dw`
or `C_(V) = int_(1)^(2) (dT)/(T) =- R int_(1)^(2) (dV)/(V)`
or `C_(V). In (T_(2))/(T_(1)) =- R In (V_(2))/(V_(1)) = R In (V_(1))/(V_(2))`
or `C_(V) log_(10).(T_(2))/(T_(1)) = R log_(10) .V_(1)//V_(2)`
or `5 xx log_(10).(303)/(293) = 2 xx log_(10) V_(2)//5`
or `5 xx log_(10) 1.034 = 2 xx log_(10) .V_(2)//5`
or `0.0725 = 2 xx log_(10) .V_(2)//5`
or `0.0362 = log_(10) .V_(2) - log_(10) 5`
or `0.0362 - 0.6990 = log_(10) V_(2)`
`V_(2) = 5.43L`
The specific heat capacity (or specific heat) of a substance is defined as the amount of heat required to raise the temperature of `1g` of the substance through `1^(@)C`.