One mole of an ideal gas at initial temperature T undergoes a quasi-static process during which the volume Vis doubled. During the process, the internal energy U obeys the equation U = aV3 , where a is a constant. The work done during this process is

Question

One mole of an ideal gas at initial temperature T undergoes a quasi-static process during which the volume Vis doubled. During the process, the internal energy U obeys the equation U = aV3 , where a is a constant. The work done during this process is (A) (3RT/2) (B) (5RT/2) (C) (5RT/3) (D) (7RT/3)

Tardigrade Admin · Accepted Answer

In the process given, internal energy is
U

= a V^{3}

\Rightarrow \frac{f n RT}{2} = a V^{3}

where,

f =

degree of freedom

= 3

(for idealgas)
and

n =

number of moles

= 1.

\Rightarrow \frac{3}{2} RT = a V^{3}

\frac{\Rightarrow 3}{2} p V = a V^{3} [∵ p V = RT]

So, pressure in this process is given by

p = \frac{2 a}{3} . V^{2}

Now, work done during the process is

W = V \int 2 V p d V = V \int 2 V \frac{2 a}{3} V^{2} d V

= \frac{2 a}{3} \times \frac{1}{3} ((2 V)^{3} - V^{3})

= \frac{2 a}{9} (7 V^{3})

= \frac{2}{9} \times 7 \times \frac{3}{2} RT [∵ a V^{3} = \frac{3}{2} R]

= \frac{7}{3} RT

Q. One mole of an ideal gas at initial temperature $T$ undergoes a quasi-static process during which the volume $V$ is doubled. During the process, the internal energy $U$ obeys the equation $U = a V^{3}$ , where $a$ is a constant. The work done during this process is

$\frac{3 RT}{2}$

$\frac{5 RT}{2}$

$\frac{5 RT}{3}$

$\frac{7 RT}{3}$

Q. One mole of an ideal gas at initial temperature T undergoes a quasi-static process during which the volume Vis doubled. During the process, the internal energy U obeys the equation U=aV3 , where a is a constant. The work done during this process is

23RT​

25RT​

35RT​

37RT​

Q. One mole of an ideal gas at initial temperature $T$ undergoes a quasi-static process during which the volume $V$ is doubled. During the process, the internal energy $U$ obeys the equation $U = a V^{3}$ , where $a$ is a constant. The work done during this process is

$\frac{3 RT}{2}$

$\frac{5 RT}{2}$

$\frac{5 RT}{3}$

$\frac{7 RT}{3}$