4 mole of helium gas at temperatures of 300 K is taken in a cylinder. (i) What is the heat required to increase its temperature to 600 K, if it is heated at constant volume (ii) what is the heat required to raise the temperature of the gas at constant pressure to 600 K ? (iii) What is the work done by the gas during the process ? Given `C _(v) = 12. 5 J//mol K, C _(p) = 20. 8 J//mol` K.

Explanation

(i) At constant volume, the quantity of heat required to raise the temperature of 4 moles gas 600 K is
` Q _(1) = n C _(v) dT`
`= 4 xx 12.5 xx (600 - 300) = 15000 J`
At constant volume the work done by the gas is `dW = PdV = 0`
(ii) At constatn pressure the quantity of heat required to raise the temperature of 4 moles of gas to 600 K is
`Q_(2) = n CpdT`
`= 4 xx 20. 8 xx (600 - 300) = 24 960 J`
Work done by the gas is `W = Q _(2) - Q _(1)`
`= 24 9 60 - 15000 = 9960J`