Thermodynamics PYQ — Page 7

The graph between two temperature scales $P$ and $Q$ is shown in the figure. Between upper fixed point and lower fixed point there are $150$ equal divisions of scale $P$ and $100$ divisions on scale $Q$. The relationship for conversion between the two scales is given by : .

The correct relation between $\gamma =\frac{{C}_{P}}{{C}_{V}}$ and temperature $T$ is :

The average kinetic energy of a molecule of the gas is

On a temperature scale '$X$', the boiling point of water is $65^{\circ}X$ and the freezing point is $-15^{\circ}X$. Assuming that the $X$ scale is linear. The equivalent temperature corresponding to $-95^{\circ}X$ on the Fahrenheit scale would be

$1\mathrm{kg}$ of water at $100^{\circ}C$ is converted into steam at $100^{\circ}C$ by boiling at atmospheric pressure. The volume of water changes from $1.00\times {10}^{-3}{m}^{3}$ as a liquid to $1.671{m}^{3}$ as steam. The change in internal energy of the system during the process will be (Given latent heat of vaporisation $=2257\mathrm{kJ}/\mathrm{kg}$, Atmospheric pressure $=1\times {10}^{5}\mathrm{Pa})$

$1g$ of a liquid is converted to vapour at $3\times {10}^{5}\mathrm{Pa}$ pressure. If $10%$ of the heat supplied is used for increasing the volume by $1600{\mathrm{cm}}^{3}$ during this phase change, then the increase in internal energy in the process will be :

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>Isothermal Process</td><td>I</td><td>Work done by the gas decreases internal energy</td></tr><tr><td>B</td><td>Adiabatic Process</td><td>II</td><td>No change in internal energy</td></tr><tr><td>C</td><td>Isochoric Process</td><td>III</td><td>The heat absorbed goes partly to increase internal energy and partly to do work</td></tr><tr><td>D</td><td>Isobaric Process</td><td>IV</td><td>No work is done on or by the gas</td></tr></tbody></table>Choose the correct answer from the options given below :

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:

Let ${\gamma }_{1}$ be the ratio of molar specific heat at constant pressure and molar specific heat at constant volume of a monoatomic gas and ${\gamma }_{2}$ be the similar ratio of diatomic gas. Considering the diatomic gas molecule as a rigid rotator, the ratio $\frac{{\gamma }_{1}}{{\gamma }_{2}}$ is:

The molar specific heat of a gas in a process PV² = constant is:

For an ideal gas undergoing isothermal process

In an Isothermal change, the change in pressure and volume of a gas can be represented for three different temperature; ${T}_{3}>{T}_{2}>{T}_{1}$ as:

If the r.m.s speed of chlorine molecule is $490m{s}^{-1}$ at ${27}^{o}C$, the r.m.s speed of argon molecules at the same temperature will be (Atomic mass of argon $=39.9u$, molecular mass of chlorine $=70.9u$)

For an ideal gas, Cp - Cv is equal to:

Heat is given to an ideal gas in an isothermal process. A. Internal energy of the gas will decrease. B. Internal energy of the gas will increase. C. Internal energy of the gas will not change. D. The gas will do positive work. E. The gas will do negative work. Choose the correct answer from the options given below :

Heat energy of $184\mathrm{kJ}$ is given to ice of mass $600g$ at $-12^{\circ}C$, Specific heat of ice is $2222.3J{\mathrm{kg}}^{–1}^{\circ}{C}^{–1}$ and latent heat of ice is $336\mathrm{kJ}{\mathrm{kg}}^{–1}$. (A) Final temperature of system will be $0^{\circ}C$ (B) Final temperature of the system will be greater than $0^{\circ}C$ (C) The final system will have a mixture of ice and water in the ratio of $5:1$ (D) The final system will have a mixture of ice and water in the ratio of $1:5$ (E) The final system will have water only Choose the correct answer from the options given below :

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: Statement I: The temperature of a gas is $-73^{\circ}C$. When the gas is heated to $527^{\circ}C$, the root mean square speed of the molecules is doubled. Statement II : The product of pressure and volume of an ideal gas will be equal to translational kinetic energy of the molecules. In the light of the above statements, choose the correct answer from the options given below:

Given below are two statements: Statement I: If heat is added to a system, its temperature must increase. Statement II: If positive work is done by a system in a thermodynamic process, its volume must increase. In the light of the above statements, choose the correct answer from the options given below

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 :

For three low density gases $A,B,C$ pressure versus temperature graphs are plotted while keeping them at constant volume, as shown in the figure  The temperature corresponding to the point $'K'$ is:

Consider two containers $A$ and $B$ containing monoatomic gases at the same Pressure $(P)$, Volume $(V)$ and Temperature $(T)$. The gas in $A$ is compressed isothermally to $\frac{1}{8}$ of its original volume while the gas in $B$ is compressed adiabatically to $\frac{1}{8}$ of its original volume. The ratio of final pressure of gas in $B$ to that of gas in $A$ is

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 $\pi =\frac{22}{7}$)

According to law of equipartition of energy the molar specific heat of a diatomic gas at constant volume where the molecule has one additional vibrational mode is :-