An ideal gas undergoes an adiabatic process obeying the relation … - Vidyadip

Question

An ideal gas undergoes an adiabatic process obeying the relation $PV^{4/3} =$ constant. If its initial temperature is $300\,\, K$ and then its pressure is increased upto four times its initial value, then the final temperature is (in Kelvin):

✓

Answer

$\mathrm{T}_{\mathrm{i}}=300 \mathrm{K} \quad \mathrm{T}_{\mathrm{f}}=?$

$\mathrm{P}_{\mathrm{i}}=\mathrm{P} \quad \mathrm{P}_{\mathrm{f}}=4 \mathrm{P}$

By gas equation we know: $-V=\frac{n R T}{P}$

$\therefore \mathrm{PV}^{4 / 3}=\mathrm{constant}$

$\Rightarrow P\left(\frac{n R T}{P}\right)^{\frac{4}{3}}=$ constant

$\Rightarrow \frac{T^{\frac{4}{3}}}{p^{\frac{1}{3}}}=$ constant

$\therefore T_{f}=\left(\frac{P_{t}}{P_{i}}\right)^{\frac{4}{3}-\frac{4}{3}} \times T_{i}=\left(\frac{4 P}{P}\right)^{\frac{1}{4}} \times 300 \mathrm{K}$

$\Rightarrow T_{f}=300 \sqrt{2} \mathrm{K}$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

NEET STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

A force applied by an engine of a train of mass $2.05 \times {10^6}\;kg$ changes its velocity from $5\;m/s$ to $25\;m/s$ in $5$ minutes. The power of the engine is ........... $MW$

The distance $x$ covered by a particle in one dimensional motion varies with time $t$ as $\mathrm{x}^{2}=\mathrm{at}^{2}+2 \mathrm{bt}+\mathrm{c.}$ If the acceleration of the particle depends on $\mathrm{x}$ as $\mathrm{x}^{-\mathrm{n}},$ where $\mathrm{n}$ is an integer, the value of $\mathrm{n}$ is

The amount of energy required to form a bubble of radius 3 cm from a soap solution is nearly: (surface tension of soap solution = $0.05 N m ^{-1}$)

Which graph represents the variation of surface tension with temperature over small temperature ranges for water

A wheatstone bridge is used to determine the value of unknown resistance $X$ by adjusting the variable resistance $Y$ as shown in the figure. For the most precise measurement of $X$, the resistances $P$ and $Q$:

A lamina is made by removing a small disc of diameter $2 \ R$ from a bigger disc of uniform mass density and radius $2 \ R$, as shown in the figure. The moment of inertia of this lamina about axes passing through $O$ and $P$ is $I _0$ and $I _{ p }$, respectively. Both these axes are perpendicular to the plane of the lamina. The ratio $\frac{ I _{ P }}{ I _0}$ to the nearest integer is:

A rider on horse back falls when horse starts running all of a sudden because

A hollow insulated conducting sphere is given a positive charge of $10\,\mu \,C$. ........$\mu \,C{m^{ - 2}}$ will be the electric field at the centre of the sphere if its radius is $2$ meters

Two particles are projected from a tower in opposite directions horizontally with speed $10\,m / s$ each. At $t=1\,s$ match the following two columns.

Column $I$	Column $II$
$(A)$ Relative acceleration between two	$(p)$ $0$ SI unit
$(B)$ Relative velocity between two	$(q)$ $5$ SI unit
$(C)$ Horizontal distance between two	$(r)$ $10$ SI unit
$(D)$ Vertical distance between two	$(s)$ $20$ SI unit

An ideal gas goes through a reversible cycle $a\to b\to c\to d$ has the $V - T$ diagram shown below. Process $d\to a$ and $b\to c$ are adiabatic.... The corresponding $P - V$ diagram for the process is (all figures are schematic and not drawn to scale)