The pressure in monoatomic gas increases linearly from ` =4xx10^(5) Nm^(-2)` to ` 8xx10^(+5) Nm^(-2)` when its volume increases from `0.2m^(3)` to `0.5m^(3)`. Calculate .
(i) Work done by the gas ,
(ii) Increase in the internal energy,
(iii) Amount of heat supplied,
(iv) Molar heat capacity of the gas `R= 8.31J mol^(-1) K^(-1)`

Answer

(i) `1.8 xx 10^(5)J (ii) 4.8 xx 10^(5)J (iii) 6.6 xx 10^(5) J (iv) 17.1 J//mole-K`

Explanation

(i) Work done by gas = `(1)/(2)(4+8) xx 10^(5)xx (0.5-0.2)`
=`1.8 xx 10^(5)J`
(ii) Increase in internal energy `DeltaU = nC_(V) DeltaT= (nR(T_(2) -T_(1)))/(gamma-1) = (P_(2)V_(2)-P_(1)V_(1))/(gamma-1)`
=`((8 xx 0.5-4 xx 0.2)xx10^(5))/((5)/(3)-1) = 4.8 xx 10^(5)J`
(iii) Amount of heat supplied `Q = DeltaU + W = 6.6 xx 10^(5)J`
(iv) Molar specific heat of the gas = `(Q)/(nDeltaT) = (6.6 xx 10^(5) xxR)/((P_(2)V_(2) - P_(1)V_(1)) = 17.1J//mole-K`