Thermodynamics PYQ — Page 3

Given below are two statements. One is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A) : With the increase in the pressure of an ideal gas, the volume falls off more rapidly in an isothermal process in comparison to the adiabatic process. Reason (R) : In isothermal process, $\mathrm{PV}=$ constant, while in adiabatic process $\mathrm{PV}^\gamma=$ constant. Here $\gamma$ is the ratio of specific heats, P is the pressure and V is the volume of the ideal gas. In the light of the above statements, choose the correct answer from the options given below :

The mean free path and the average speed of oxygen molecules at 300 K and 1 atm are $3 \times 10^{-7} \mathrm{~m}$ and $600 \mathrm{~m} / \mathrm{s}$ respectively. Find the frequency of its collisions.

Which of the following figure represents the relation between Celsius and Fahrenheit temperatures ?

An amount of ice of mass $10^{-3} \mathrm{~kg}$ and temperature $-10^{\circ} \mathrm{C}$ is transformed to vapour of temperature $110^{\circ} \mathrm{C}$ by applying heat. The total amount of work required for this conversion is, (Take, specific heat of ice $=2100 \mathrm{Jkg}^{-1} \mathrm{~K}^{-1}$, specific heat of water $=4180 \mathrm{Jkg}^{-1} \mathrm{~K}^{-1}$, specific heat of steam $=1920 \mathrm{Jkg}^{-1} \mathrm{~K}^{-1}$, Latent heat of ice $=3.35 \times 10^5 \mathrm{Jkg}^{-1}$ and Latent heat of steam $=2.25 \times 10^6$ $\mathrm{Jkg}^{-1}$ )

The magnitude of heat exchanged by a system for the given cyclic process ABCA (as shown in figure) is (in SI unit) : 

 Using the given $\mathrm{P}-\mathrm{V}$ diagram, the work done by an ideal gas along the path ABCD is :

A wire of length 10 cm and diameter 0.5 mm is used in a bulb. The temperature of the wire is $1727^{\circ} \mathrm{C}$ and power radiated by the wire is 94.2 W. Its emissivity is $\frac{x}{8}$ where $x=$_______ (Given $\sigma=6.0 \times 10^{-8} \mathrm{~W} \mathrm{~m}^{-2} \mathrm{~K}^{-4}, \pi=3.14$ and assume that the emissivity of wire material is same at all wavelength.)

Given below are two statements. One is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A) : In an insulated container, a gas is adiabatically shrunk to half of its initial volume. The temperature of the gas decreases. Reason (R): Free expansion of an ideal gas is an irreversible and an adiabatic process. In the light of the above statements, choose the correct answer from the options given below :

An ideal gas has undergone through the cyclic process as shown in the figure. Work done by the gas in the entire cycle is ______ $\times 10^{-1} \mathrm{~J}$. (Take $\pi=3.14$) 

During the melting of a slab of ice at 273 K at atmospheric pressure :

For a diatomic gas, if $\gamma_1=\left(\frac{C p}{C v}\right)$ for rigid molecules and $\gamma_2=\left(\frac{C p}{C v}\right)$ for another diatomic molecules, but also having vibrational modes. Then, which one of the following options is correct ? (Cp and Cv are specific heats of the gas at constant pressure and volume)

A container of fixed volume contains a gas at \(27^{\circ} \mathrm{C}\). To double the pressure of the gas, the temperature of gas should be raised to ______ \({ }^{\circ} \mathrm{C}\).

The helium and argon are put in the flask at the same room temperature ( 300 K). The ratio of average kinetic energies (per molecule) of helium and argon is : (Give : Molar mass of helium $=4 \mathrm{~g} / \mathrm{mol}$, Molar mass of argon $=40 \mathrm{~g} / \mathrm{mol}$)

A gas is kept in a container having walls which are thermally non-conducting. Initially the gas has a volume of $800 \mathrm{~cm}^3$ and temperature $27^{\circ} \mathrm{C}$. The change in temperature when the gas is adiabatically compressed to $200 \mathrm{~cm}^3$ is : (Take $\gamma=1.5: \gamma$ is the ratio of specific heats at constant pressure and at constant volume)

An ideal gas exists in a state with pressure $P_0$ volume $\mathrm{V}_0$.It is isothermally expanded to 4 times of its initial volume $\left(\mathrm{V}_0\right)$, then isobarically compressed to its original volume. Finally the system is heated isochorically to bring it to its initial state. The amount of heat exchanged in this process is :

For a particular ideal gas which of the following graphs represents the variation of mean squared velocity of the gas molecules with temperature?

Match List-I with List-II. $\begin{array}{|l|l|l|l|} \hline & \text{List-I} & & \text{List-II} \\ \hline \text{(A)} & \text{Isothermal} & \text{(I)} & \Delta \mathrm{W} \text{(work done)} =0 \\ \hline \text{(B)} & \text{Adiabatic} & \text{(II)} & \Delta \mathrm{Q} \text{(supplied heat)} =0 \\ \hline \text{(C)} & \text{Isobaric} & \text{(III)} & \begin{array}{l}\Delta \mathrm{U} \text{(change in internal} \\ \text{energy} \neq 0\end{array} \\ \hline \text{(D)} & \text{Isochoric} & \text{(IV)} & \Delta \mathrm{U}=0 \\ \hline\end{array}$ Choose the correct answer from the options given below :

 A poly-atomic molecule ( $C_V=3 R, C_P=4 R$, where $R$ is gas constant) goes from phase space point $\mathrm{A}\left(\mathrm{P}_{\mathrm{A}}=10^5 \mathrm{~Pa}, \mathrm{~V}_{\mathrm{A}}=4 \times 10^{-6} \mathrm{~m}^3\right)$ to point $\mathrm{B}\left(\mathrm{P}_{\mathrm{B}}=5 \times 10^4 \mathrm{~Pa}, \mathrm{~V}_{\mathrm{B}}=6 \times 10^{-6} \mathrm{~m}^3\right)$ to point $\mathrm{C}\left(\mathrm{P}_{\mathrm{C}}=10^4\right.$ $\left.\mathrm{Pa}, \mathrm{V}_{\mathrm{C}}=8 \times 10^{-6} \mathrm{~m}^3\right)$. A to B is an adiabatic path and $B$ to $C$ is an isothermal path. The net heat absorbed per unit mole by the system is :

There are two vessels filled with an ideal gas where volume of one is double the volume of other. The large vessel contains the gas at 8 kPa at 1000 K while the smaller vessel contains the gas at 7 kPa at 500 K. If the vessels are connected to each other by a thin tube allowing the gas to flow and the temperature of both vessels is maintained at 600 K , at steady state the pressure in the vessels will be (in kPa).

Match List-I with List-II. \(\begin{array}{|l|l|l|l|} \hline & \text{List - I} & & \text{List - II} \\ \hline \text { (A) } & \text { Isobaric } & \text { (I) } & \Delta Q=\Delta W \\ \hline \text { (B) } & \text { Isochoric } & \text { (II) } & \Delta Q=\Delta U \\ \hline \text { (C) } & \text { Adiabatic } & \text { (III) } & \Delta Q=\text { zero } \\ \hline \text { (D) } & \text { Isothermal } & \text { (IV) } & \Delta Q=\Delta U+P \Delta V \\ \hline \end{array}\) $\Delta \mathrm{Q}=$ Heat supplied $\Delta \mathrm{W}=$ Work done by the system $\Delta \mathrm{U}=$ Change in internal energy $\mathrm{P}=$ Pressure of the system $\Delta \mathrm{V}=$ Change in volume of the system Choose the correct answer from the options given below:

An ideal gas goes from an initial state to final state. During the process, the pressure of gas increases linearly with temperature. A. The work done by gas during the process is zero. B. The heat added to gas is different from change in its internal energy. C. The volume of the gas is increased. D. The internal energy of the gas is increased. E. The process is isochoric (constant volume process) Choose the correct answer from the options given below:

A monoatomic gas having $\gamma=\frac{5}{3}$ is stored in a thermally insulated container and the gas is suddenly compressed to $\left(\frac{1}{8}\right)^{\text {th }}$ of its initial volume. The ratio of final pressure and initial pressure is: ( $\gamma$ is the ratio of specific heats of the gas at constant pressure and at constant volume)

A cup of coffee cools from $90^{\circ} \mathrm{C}$ to $80^{\circ} \mathrm{C}$ in t minutes when the room temperature is $20^{\circ} \mathrm{C}$. The time taken by the similar cup of coffee to cool from $80^{\circ} \mathrm{C}$ to $60^{\circ} \mathrm{C}$ at the same room temperature is :

An ideal gas initially at $0^{\circ} \mathrm{C}$ temperature, is compressed suddenly to one fourth of its volume. If the ratio of specific heat at constant pressure to that at constant volume is $3 / 2$, the change in temperature due to the thermodynamic process is _____ K.