Thermodynamics PYQ — Page 8

Match List I with List II: <table class="pyq-table"><tbody><tr><td></td><td>List I</td><td></td><td>List II</td></tr><tr><td>(A)</td><td>$3$ Translational degrees of freedom</td><td>(I)</td><td>Monoatomic gases</td></tr><tr><td>(B)</td><td>$3$ Translational, $2$ rotational degrees of freedoms</td><td>(II)</td><td>Polyatomic gases</td></tr><tr><td>(C)</td><td>$3$ Translational, $2$ rotational and $1$ vibrational degrees of freedom</td><td>(III)</td><td>Rigid diatomic gases</td></tr><tr><td>(D)</td><td>$3$ Translational, $3$ rotational and more than one vibrational degrees of freedom</td><td>(IV)</td><td>Nonrigid diatomic gases</td></tr></tbody></table>Choose the correct answer from the options given below:

A thin rod having a length of $1m$ and area of cross-section $3\times {10}^{-6}{m}^{2}$ is suspended vertically from one end. The rod is cooled from $210^{\circ}C$ to $160^{\circ}C$. After cooling, a mass $M$ is attached at the lower end of the rod such that the length of rod again becomes $1m$. Young's modulus and coefficient of linear expansion of the rod are $2\times {10}^{11}N{m}^{-2}$ and $2\times {10}^{-5}{K}^{-1}$, respectively. The value of $M$ is ______ $\mathrm{kg}$. (Take $g=10m{s}^{-2}$)

Heat energy of $735J$ is given to a diatomic gas allowing the gas to expand at constant pressure. Each gas molecule rotates around an internal axis but do not oscillate. The increase in the internal energy of the gas will be:

Given below are two statements. One is labelled as Assertion A and the other is labelled as Reason R. Assertion A : If $dQ$ and $dW$ represent the heat supplied to the system and the work done on the system respectively. Then according to the first law of thermodynamics $dQ=dU-dW$. Reason R : First law of thermodynamics is based on law of conservation of energy. In the light of the above statements, choose the correct answer from the option given below :

The $\mathrm{rms}$ speed of oxygen molecule in a vessel at particular temperature is ${(1+\frac{5}{x})}^{\frac{1}{2}}v,$ when $v$ is the average speed of the molecule. The value of $x$ will be: (take $\pi =\frac{22}{7}$)

The mean free path of molecules of a certain gas at STP is $1500d$, where $d$is the diameter of the gas molecules. While maintaining the standard pressure, the mean free path of the molecules at $373K$ is approximately:

The average kinetic energy of a molecule of the gas is

The number of air molecules per ${\mathrm{cm}}^{3}$ is increased from $3\times {10}^{19}$ to $12\times {10}^{19}.$ The ratio of collision frequency of air molecules before and after the increase in number respectively is :

Three vessels of equal volume contain gases at the same temperature and pressure. The first vessel contains neon (monoatomic), the second contains chlorine (diatomic) and third contains uranium hexafluoride (polyatomic). Arrange these on the basis of their root mean square speed $({v}_{rms})$ and choose the correct answer from the options given below:

A flask contains Hydrogen and Argon in the ratio $2:1$ by mass. The temperature of the mixture is $30^{\circ}C$. The ratio of average kinetic energy per molecule of the two gases $(\frac{{K}_{\mathrm{argon}}}{{K}_{\mathrm{hydrogen}}})$ is: (Given : Atomic Weight of $Ar=39.9$)

The root mean square speed of molecules of nitrogen gas at $27^{\circ}C$ is approximately: (Given mass of a nitrogen molecule $=4.6\times {10}^{-26}\mathrm{kg}$ and take Boltzmann constant ${k}_{B}=1.4\times {10}^{-23}J{K}^{-1}$ )

At $300K$, the rms speed of oxygen molecules is $\sqrt{\frac{\alpha +5}{\alpha }}$ times to that of its average speed in the gas. Then, the value of $\alpha$ will be (use $\pi =\frac{22}{7}$)

The temperature of an ideal gas is increased from $200K$ to $800K$. If r.m.s. speed of gas at $200K$ is ${v}_{0}$. Then, r.m.s. speed of the gas at $800K$ will be:

A hole is drilled in a metal sheet. At $27^{\circ}C$, the diameter of hole is $5\mathrm{cm}$. When the sheet is heated to $177^{\circ}C$, the change in the diameter of hole is $d\times {10}^{-3}\mathrm{cm}$ . The value of $d$ will be _____, if coefficient of linear expansion of the metal is $1.6\times {10}^{-5}/C\circ$

The thermodynamic process, in which internal energy of the system remains constant is

Same gas is filled in two vessels of the same volume at the same temperature. If the ratio of the number of molecules is $1:4$, then $A$. The r.m.s. velocity of gas molecules in two vessels will be the same. $B$. The ratio of pressure in these vessels will be $1:4$. $C$. The ratio of pressure will be $1:1$. $D$. The r.m.s. velocity of gas molecules in two vessels will be in the ratio of $1:4$.

Statement - I : When $\mu$ amount of an ideal gas undergoes adiabatic change from state $({P}_{1},{V}_{1},{T}_{1})$ to state $({P}_{2},{V}_{2},{T}_{2})$, then work done is $W=\frac{\mu R({T}_{2}-{T}_{1})}{1-\gamma }$, where $\gamma =\frac{{C}_{P}}{{C}_{V}}$ and $R=$ universal gas constant. Statement - II : In the above case, when work is done on the gas, the temperature of the gas would rise.

The pressure ${P}_{1}$ and density ${d}_{1}$ of diatomic gas $(\gamma =\frac{7}{5})$ changes suddenly to ${P}_{2}(>{P}_{1})$ and ${d}_{2}$ respectively during an adiabatic process. The temperature of the gas increases and becomes____times of its initial temperature. (given $\frac{{d}_{2}}{{d}_{1}}=32$)

The efficiency of a Carnot engine working between 127°C and 27°C is:

A gas has $n$ degrees of freedom. The ratio of specific heat of gas at constant volume to the specific heat of gas at constant pressure will be

What will be the effect on the root mean square velocity of oxygen molecules if the temperature is doubled and oxygen molecule dissociates into atomic oxygen?

The root mean square speed of smoke particles of mass $5\times {10}^{-17}\mathrm{kg}$ in their Brownian motion in air at NTP is approximately. [Given $k=1.38\times {10}^{-23}J{K}^{-1}$]

Starting with the same initial conditions, an ideal gas expands from volume ${V}_{1}$ to ${V}_{2}$ in three different ways. The work done by the gas is ${W}_{1}$ if the process is purely isothermal, ${W}_{2}$, if the process is purely adiabatic and ${W}_{3}$ if the process is purely isobaric. Then, choose the correct option

A geyser heats water flowing at a rate of $2.0\mathrm{kg}$ per minute from $30^{\circ}C$ to $70^{\circ}C$. If geyser operates on a gas burner, the rate of combustion of fuel will be _____ $g{\mathrm{min}}^{-1}$. [Heat of combustion $=8\times {10}^{3}{\mathrm{Jg}}^{-1}$, Specific heat of water $=4.2{\mathrm{Jg}}^{-1}{C\circ }^{-1}$]