Question

N moles of an ideal gas undergoes a process in which the temperature changes with volume as t=kv2 the work done by the gas as the temperature changes from t to 4t is

Answer 1

A ideal gas undergoes a process in which the temperature changes with volume as T = kV² ........(1)

from ideal gas equation,

PV = NRT, where N is number of moles [given]

PV = NR(KV²) [ from equation (1), ]

P = KNRV

or, PV^-1 = KNR = constant.

comparing with equation, $\bf{PV^{\alpha}=constant}$

we get, $\alpha=-1$

now, workdone is given for this process , W =- $\frac{NR\Delta T}{\alpha-1}$

= -NR(4T - T)/(-1-1)

= 3NRT/2

hence, workdone by the gas is $\frac{3}{2}NRT$