MCQ
Work done per mol in an isothermal change is
- A$RT{\log _{10}}\frac{{{V_2}}}{{{V_1}}}$
- B$RT{\log _{10}}\frac{{{V_1}}}{{{V_2}}}$
- ✓$RT{\log _e}\frac{{{V_2}}}{{{V_1}}}$
- D$RT{\log _e}\frac{{{V_1}}}{{{V_2}}}$
✓
Answer
Correct option: C.
$RT{\log _e}\frac{{{V_2}}}{{{V_1}}}$
c
(c)For isothermal process $PV = RT \Rightarrow P = \frac{{RT}}{V}$
$\therefore $W$ = PdV = \int_{\,{V_1}}^{\,{V_2}} {\frac{{RT}}{V}dV = RT} {\log _e}\frac{{{V_2}}}{{{V_1}}}$
(c)For isothermal process $PV = RT \Rightarrow P = \frac{{RT}}{V}$
$\therefore $W$ = PdV = \int_{\,{V_1}}^{\,{V_2}} {\frac{{RT}}{V}dV = RT} {\log _e}\frac{{{V_2}}}{{{V_1}}}$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
The velocity of a particle performing simple harmonic motion, when it passes through its mean position is
The magnitude of pairs of displacement vectors are given. Which pair of displacement vectors cannot be added to give a resultant vector of magnitude $13\, cm$?
→A metal ball of surface area $200\;c{m^2}$ and temperature ${527^o}C$ is surrounded by a vessel at ${27^o}C$. If the emissivity of the metal is $0.4$ , then the rate of loss of heat from the ball is .......... $joules $ approx. $(\sigma = 5.67 \times {10^{ - 8}}J/{m^2}\; - s - {k^4})$
→If speed of sound in air in $330 \,m / s$ then, find the number of tones present in an open organ pipe of length $1\, m$ whose frequency if $\leq 1000$.
→The masses of blocks A and B are $m$ and $M$ respectively. Between $A$ and $B$, there is a constant frictional force $F$ and $B$ can slide on a smooth horizontal surface. A is set in motion with velocity while $B$ is at rest. What is the distance moved by A relative to $B$ before they move with the same velocity?
→If the temperature of the sun becomes twice its present temperature, then
A child weighing $25 \,kg$ slides down a rope hanging from a branch of a tall tree. If the force of friction acting against him is $200 \,N$, the acceleration of child is ........... $m / s^2$ $\left(g=10 \,m / s ^2\right)$
→If the angular momentum of a rotating body is increased by $200\ \%$, then its kinetic energy of rotation will be increased by .......... $\%$
→At a moment in a progressive wave, the phase of a particle executing $S.H.M.$ is $\frac{\pi }{3}$. Then the phase of the particle $15 cm$ ahead and at the time $\frac{T}{2}$ will be, if the wavelength is $60 cm$
→Change in temperature of the medium changes: