Question
Two gases have the same initial pressure, volume and temperatue. They expand to the same final volume, one adiabatically and the other isothermally, if the two gases are compressed to the same final volume
✓
Answer
Work done is equal to area under the P-V graph, thus work done by gas is greater for isothermal process.
For isothermal process: $T_2=T_0$
For adibatic process: $T_0\left(V_0\right)^{\gamma-1}=T(V)^{\gamma-1}$
As $V > V _0 \Rightarrow T < T _0$
Thus final temp. is greater for isothermal process.
For isothermal process: $P_0 V_0=P_i V \Rightarrow P_1=P_0 \frac{V_0}{V}$
For adibatic process: $P_0\left( V _0\right)^\gamma= P _2( V )^y$
$\Rightarrow P _2= P _0\left(\frac{ V _0}{ V }\right)^\gamma$
As $\gamma > 1$ (always) $\Rightarrow P_1 > P_2$
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 root mean square speed of hydrogen molecules of an ideal hydrogen gas kept in a gas chamber at $0°C$ is $3180$ metres/second. The pressure on the hydrogen gas is ..... $atm$ (Density of hydrogen gas is $8.99 \times {10^{ - 2}}\,kg/{m^3}$, $1$ atmosphere $ = 1.01 \times {10^5}\,N/{m^2})$
→Find wrong statement
A circular conducting coil of radius $1\, {m}$ is being heated by the change of magnetic field $\vec {B}$ passing perpendicular to the plane in which the coil is laid. The resistance of the coil is $2\, \mu\, \Omega$. The magnetic field is slowly switched off such that its magnitude changes in time as
→$B=\frac{4}{\pi} \times 10^{-3}\, {T}\left(1-\frac{{t}}{100}\right)$
The energy dissipated by the coil before the magnetic field is switched off completely is $E=.....\,{m} J.$
A small fish $0.4\, m$ below the surface of a lake, is viewed through a simple converging lens of focal length $3\, m$. The lens is kept at $0.2\, m$ above the water surface such that fish lies on the optical axis of the lens. The image of the fish seen by observer will be at $\left( {{\mu _{water}} = \frac{4}{3}} \right)$
→In the given figure a ring of mass $m$ is kept on a horizontal surface while a body of equal mass $'m'$ attached through a string, which is wounded on the ring. When the system is released the ring rolls without slipping. Consider the following statements and choose the correct option.
→$(i)$ acceleration of the centre of mass of ring is $\frac{g}{3}$
$(ii)$ acceleration of the hanging particle is $\frac{2g}{3}$
$(iii)$ frictional force (on the ring) acts along forward direction
$(iv)$ frictional force (on the ring) acts along backward direction
Your friend driving his car overtakes your car on the highway. Which of the following statement must be true at the instant he is passing you? Assume the cars as point particles.
On mixing the salt in water, the surface tension of water will
A spring block system in horizontal oscillation has a time-period $T$. Now the spring is cut into four equal parts and the block is re-connected with one of the parts. The new time period of vertical oscillation will be
→The resistance $R=V / I$ where $V=(100 \pm 5)\;V$ and $I=(10 \pm 0.2) \;A$. Find the percentage error in $R .$
→The diagram below shows the change in the length $X$ of a thin uniform wire caused by the application of stress $F$ at two different temperatures $T_1$ and $T_2$. The variation shown suggests that
→