Thermodynamics PYQ — Page 12

Which of the following graphs represent the behaviour of an ideal gas? Symbols have their usual meaning.

A container is divided into two chambers by a partition. The volume of first chamber is $4.5\mathrm{litre}$ and second chamber is $5.5\mathrm{litre}$. The first chamber contain $3.0$ moles of gas at pressure $2.0\mathrm{atm}$ and second chamber contain $4.0$ moles of gas at pressure $3.0\mathrm{atm}$. After the partition is removed and the mixture attains equilibrium, then, the common equilibrium pressure existing in the mixture is $x\times {10}^{-1}\mathrm{atm}$. Value of $x$ (nearest integer) is

If one mole of an ideal gas at $({P}_{1},{V}_{1})$ is allowed to expand reversibly and isothermally ($A$ to $B$) its pressure is reduced to one-half of the original pressure (see figure). This is followed by a constant volume cooling till its pressure is reduced to one-fourth of the initial value $(B\rightarrow C).$ Then it is restored to its initial state by a reversible adiabatic compression ($C$ to $A$). The net workdone by the gas is equal to: 

What will be the average value of energy for a monoatomic gas in thermal equilibrium at temperature $T?$

What will be the average value of energy along one degree of freedom for an ideal gas in thermal equilibrium at a temperature $T?$ (${k}_{B}$ is Boltzmann constant)

Calculate the value of the mean free path $(\lambda )$ for oxygen molecules at temperature $27^{\circ}C$ and pressure $1.01\times {10}^{5}\mathrm{Pa}$. Assume the molecular diameter $0.3\mathrm{nm}$ and the gas is ideal. $(k=1.38\times {10}^{-23}J{K}^{-1})$

The root-mean-square speed of molecules of a given mass of a gas at $27^{\circ}C$ and $1$ atmosphere pressure is $200m{s}^{-1}.$ The root-mean-square speed of molecules of the gas at $127^{\circ}C$ and $2$ atmosphere pressure is $\frac{x}{\sqrt{3}}m{s}^{-1}.$ The value of $x$ will be __________.

A diatomic gas, having ${C}_{P}=\frac{7}{2}R$ and ${C}_{V}=\frac{5}{2}R,$ is heated at constant pressure. The ratio $dU:dQ:dW$

A uniform heating wire of resistance $36\Omega$ is connected across a potential difference of $240V.$ The wire is then cut into half and a potential difference of $240V$ is applied across each half separately. The ratio of power dissipation in first case to the total power dissipation in the second case would be $1:x,$ where $x$ is

The internal energy $(U)$, pressure $(P)$ and volume $(V)$ of an ideal gas are related as $U=3PV+4.$ The gas is

Consider a mixture of gas molecule of types $A,B$ and $C$ having masses ${m}_{A}<{m}_{B}<{m}_{C}.$ The ratio of their root mean square speeds at normal temperature and pressure is:

Two thin metallic spherical shells of radii ${r}_{1}$ and ${r}_{2}({r}_{1}<{r}_{2})$ are placed with their centres coinciding. A material of thermal conductivity $K$ is filled in the space between the shells. The inner shell is maintained at temperature ${\theta }_{1}$ and the outer shell at temperature ${\theta }_{2}({\theta }_{1}<{\theta }_{2}).$ The rate at which heat flows radially through the material is :

The temperature of equal masses of three different liquids $x,y$ and $z$ are $10^{\circ}C,20^{\circ}C$ and $30^{\circ}C$ respectively. The temperature of mixture when $x$ is mixed with $y$ is $16^{\circ}C$ and that when $y$ is mixed with $z$ is $26^{\circ}C$. The temperature of mixture when $x$ and $z$ are mixed will be :

Due to cold weather, a $1m$ water pipe of cross-sectional area $1{\mathrm{cm}}^{2}$ is filled with ice at $-10^{\circ}C.$ Resistive heating is used to melt the ice. Current of $0.5A$ is passed through $4k\Omega$ resistance. Assuming that all the heat produced is used for melting, what is the minimum time required? (Given latent heat of fusion for water/ice$=3.33\times {10}^{5}J{\mathrm{kg}}^{-1},$ specific heat of ice $=2\times {10}^{3}J{\mathrm{kg}}^{-1}^{\circ}{C}^{-1}$ and density of ice $={10}^{3}\mathrm{kg}{m}^{-3})$

If one mole of the polyatomic gas is having two vibrational modes and $\beta$ is the ratio of molar specific heats for polyatomic gas $(\beta =\frac{{C}_{P}}{{C}_{v}})$ then the value of $\beta$ is :

The entropy of any system is given by, $S={\alpha }^{2}\beta \mathrm{ln}[\frac{\mu \mathrm{kR}}{J{\beta }^{2}}+3]$ where $\alpha$ and $\beta$ are the constants. $\mu ,J,k$ and $R$ are number of moles, mechanical equivalent of heat, Boltzmann's constant and gas constant, respectively. $[\text{Take }S=\frac{dQ}{T}]$ Choose the incorrect option from the following:

The correct relation between the degrees of freedom $f$ and the ratio of specific heat $\gamma$ is:

Match List $I$ with List $\mathrm{II}.$ <table class="pyq-table"><tbody><tr><td></td><td>List $I$</td><td></td><td>List $\mathrm{II}$</td></tr><tr><td>(a)</td><td>Isothermal</td><td>(i)</td><td>Pressure constant</td></tr><tr><td>(b)</td><td>Isochoric</td><td>(ii)</td><td>Temperature constant</td></tr><tr><td>(c)</td><td>Adiabatic</td><td>(iii)</td><td>Volume constant</td></tr><tr><td>(d)</td><td>Isobaric</td><td>(iv)</td><td>Heat content is constant</td></tr></tbody></table>Choose the correct answer from the options given below:

An ideal gas is expanding such that $P{T}^{3}=$ constant. The coefficient of volume expansion of the gas is:

Two ideal polyatomic gases at temperatures ${T}_{1}$ and ${T}_{2}$ are mixed so that there is no loss of energy. If ${F}_{1}$ and ${F}_{2},{m}_{1}$ and ${m}_{2},{n}_{1}$ and ${n}_{2}$ be the degrees of freedom, masses, number of molecules of the first and second gas respectively, the temperature of mixture of these two gases is:

One mole of an ideal gas at $27^{\circ}C$ is taken from $A$ to $B$ as shown in the given $PV$ indicator diagram. The work done by the system will be _______ $\times {10}^{-1}J.$ [Given, $R=8.3J{\mathrm{mole}}^{-1}K,\mathrm{ln}2=0.6931$] (Round off to the nearest integer) (Round off to the nearest integer) 

The volume $V$ of a given mass of monoatomic gas changes with temperature $T$ according to the relation $V=K{T}^{\frac{2}{3}}$. The workdone when temperature changes by $90K$ will be $xR$. The value of $x$ is [$R$ universal gas constant ]

$n$ mole of a perfect gas undergoes a cyclic process $ABCA$ (see figure) consisting of the following processes. $A\rightarrow B:$ Isothermal expansion at temperature $T$ so that the volume is doubled from ${V}_{1}$ to ${V}_{2}=2{V}_{1}$ and pressure changes from ${P}_{1}$ to ${P}_{2}$ $B\rightarrow C:$ Isobaric compression at pressure ${P}_{2}$ to initial volume ${V}_{1}.$ $C\rightarrow A:$ Isochoric change leading to change of pressure from ${P}_{2}$ to ${P}_{1}$ Total work done in the complete cycle $ABCA$ is: 

Given below are two statements: Statement I: In a diatomic molecule, the rotational energy at a given temperature obeys Maxwell's distribution. Statement II : In a diatomic molecule, the rotational energy at a given temperature equals the translational kinetic energy for each molecule. In the light of the above statements, choose the correct answer from the options given below: