Thermodynamics PYQ — Page 14

Under an adiabatic process, the volume of an ideal gas gets doubled. Consequently, the mean collision time between the gas molecule changes from ${\tau }_{1}$ to ${\tau }_{2}$ . If $\frac{{C}_{P}}{{C}_{v}}=\gamma$ for this gas then a good estimate for $\frac{{\tau }_{2}}{{\tau }_{1}}$ is given by

A balloon filled with helium $(32^{\circ}C \mathrm{and} 1.7\mathrm{atm})$ bursts. Immediately after wards the expansion of helium can be considered as :

The change in the magnitude of the volume of an ideal gas when a small additional pressure $\Delta P$ is applied at a constant temperature, is the same as the change when the temperature is reduced by a small quantity $\Delta T$ at constant pressure. The initial temperature and pressure of the gas were $300K$and $2\mathrm{atm}$ respectively. If $|\Delta T|=C|\Delta P|$ then value of $C$ in $(K/\mathrm{atm})$ is __________

Two different wires having lengths ${L}_{1}$ and ${L}_{2}$ and respective temperature coefficient of linear expansion ${\alpha }_{1}$ and ${\alpha }_{2},$ are joined end-to-end. Then the effective temperature coefficient of linear expansion is :

When the temperature of a metal wire is increased from $0ºC\mathrm{to}10ºC$, its length increases by $0.02%$.The percentage change in its mass density will be closed to:

Three containers ${C}_{1},{C}_{2}$ and ${C}_{3}$ have water at different temperatures. The table below shows the final temperature $T$ when different amounts of water (given in liters) are taken from each container and mixed (assume no loss of heat during the process) <table class="pyq-table"><tbody><tr><th>${C}_{1}$</th><th>${C}_{2}$</th><th>${C}_{3}$</th><th>$T$</th></tr><tr><td>$1l$</td><td>$2l$</td><td>$--$</td><td>${60}^{o}C$</td></tr><tr><td>$--$</td><td>$1l$</td><td>$2l$</td><td>${30}^{o}C$</td></tr><tr><td>$2l$</td><td>$--$</td><td>$1l$</td><td>${60}^{o}C$</td></tr><tr><td>$1l$</td><td>$1l$</td><td>$1l$</td><td>$\theta$</td></tr></tbody></table> The value of $\theta$ (in ${}^{o}C$ to the nearest integer) is___________

Nitrogen gas is at $300^{\circ}C$ temperature. The temperature (in $K$ ) at which the rms speed of a ${H}_{2}$ molecule would be equal to the rms speed of a nitrogen molecule, is $\ldots \ldots \ldots .$ (Molar mass of ${N}_{2}$ gas $28g$ ).

Assuming the nitrogen molecule is moving with $r.m.s$. velocity at $400K$, the de-Broglie wave length of nitrogen molecule is close to : (Given : nitrogen molecule weight : $4.64\times {10}^{-26} \mathrm{kg}$, Boltzman constant : $1.38\times {10}^{-23} J{K}^{-1}$, Planck constant : $6.63\times {10}^{-34} Js$)

To raise the temperature of a certain mass of gas by $50^{\circ}C$ at a constant pressure,$160$ calories of heat is required. When the same mass of gas is cooled by $100^{\circ}C$ at constant volume,$240$ calories of heat is released. How many degrees of freedom does each molecule of this gas have (assume gas to be ideal)?

A litre of dry air at STP expands adiabatically to a volume of $3$ litres. If $\gamma =1.40,$ the work done by air is: $({3}^{1.4}=4.6555)$ [Take air to be an ideal gas]

The plot that depicts the behavior of the mean free time $\tau$ (time between two successive collisions) for the molecules of an ideal gas, as a function of temperature $(T),$ qualitatively, is: (Graphs are schematic and not drawn to scale)

Number of molecules in a volume of $4{\mathrm{cm}}^{3}$ of a perfect monoatomic gas at some temperature T and at a pressure of $2\mathrm{cm}$ of mercury is close to? (Given, mean kinetic energy of a molecule (at T) is $4\times {10}^{-14}\mathrm{erg},g=980\mathrm{cm}{s}^{-2}$ density of mercury $=13.6g{\mathrm{cm}}^{-3}$)

Three different processes that can occur in an ideal monoatomic gas are shown in the $P$ vs $V$ diagram. The paths are labelled as $A\rightarrow B,A\rightarrow C$ and $A\rightarrow D$. The change in internal energies during these process are taken as ${E}_{AB},{E}_{AC}$ and ${E}_{AD}$ and the work done as ${W}_{AB},{W}_{AC}$ and ${W}_{AD}$. The correct relation between these parameters are: 

A closed vessel contains $0.1$ mole of a monoatomic ideal gas at $200\text{ K}$. If $0.05$ mole of the same gas at $400K$ is added to it, the final equilibrium temperature (in $\text{K}$) of the gas in the vessel will be close to ______

Two gases - argon (atomic radius $0.07nm,$ atomic weight $40$ ) and xenon (atomic radius $0.1nm,$ atomic weight $140$ ) have the same number density and are at the same temperature. The ratio of their respective mean free times is closest to:

 Consider a gas of triatomic molecules. The molecules are assumed to be triangular and made of massless rigid rods whose vertices are occupied by atoms. The internal energy of a mole of the gas at temperature T is:

Three rods of identical cross-section and length are made of three different materials of thermal conductivity ${K}_{1},{K}_{2}$ and ${K}_{3}$, respectively. They are joined together at their ends to make a long rod (see figure). One end of the long rod is maintained at $100^{\circ}C$ and the other at $0^{\circ}C$ (see figure). If the joints of the rod are at $70^{\circ}C$ and $20^{\circ}C$ in steady and there is no loss of energy from the surface of the rod, the correct relationship between ${K}_{1},{K}_{2}$ and ${K}_{3}$ is : 

Two moles of an ideal gas, with $\frac{{C}_{P}}{{C}_{V}}=\frac{5}{3}$, are mixed with three moles of another ideal gas $\frac{{C}_{P}}{{C}_{V}}=\frac{4}{3}$. The value of $\frac{{C}_{P}}{{C}_{V}}$ for the mixture is

The specific heat of water $=4200\text{ J}$ ${\text{kg}}^{–1}{\text{ K}}^{–1}$ and the latent heat of ice $=3.4\times {10}^{5}\text{ J}$ k${\text{g}}^{–1}$. $100$ grams of ice at $0{ }^{\text{o}}\text{C}$ is placed in $200\text{ g}$ of water at $25{ }^{\text{o}}\text{C}$. The amount of ice that will melt as the temperature of water reaches $0{ }^{\text{o}}\text{C}$ is close to (in grams)

Consider two ideal diatomic gases $A$ and $B$ at some temperature $T$ . Molecules of the gas $A$ are rigid, and have a mass $m$ . Molecules of the gas $B$ have an additional vibrational mode and have a mass $\frac{m}{4}$ . The ratio of the specific heats ${({C}_{V}^{})}_{A}\text{and }{({C}_{V}^{})}_{B}$ of gas $A$ and $B,$ respectively is:

$M$ grams of steam at ${100}^{o}C$ is mixed with $200g$ of ice at its melting point in a thermally insulated container. If it produces liquid water at ${40}^{o}C$ [heat of vaporization of water is $540cal/g$ and heat of fusion of ice is $80cal/g$ ], the value of $M$ is ________

Starting at temperature $300K,$ one mole of an ideal diatomic gas $(\gamma =1.4)$ is first compressed adiabatically from volume ${V}_{1}$ to ${V}_{2}=\frac{{V}_{1}}{16}.$ It is then allowed to expand isobarically to volume $2{V}_{2}$ . If all the processes are the quasi-static then the final temperature of the gas (in ${}^{o}K$ ) is (to the nearest integer) ___________.

A non-isotropic solid metal cube has coefficients of linear expansion as: $5\times { 10}^{ -5} / {}^{\text{o}} \text{C}$ along the x-axis and $5\times { 10}^{ -6} / {}^{\text{o}} \text{C}$ along the y and the z-axis. If the coefficient of volume expansion of the solid is $\text{C}\times { 10}^{ -6} / {}^{\text{o}} \text{C}$ then the value of $C$ is _____________

A bullet of mass $5\mathrm{gram}$, travelling with a speed of $210m{s}^{-1}$ strikes a fixed wooden target. One half of its kinetic energy is converted into heat in the wood. The rise of temperature of the bullet if the specific heat of its material is $0.030{(\mathrm{gram}^{\circ}C)}^{-1}(1\mathrm{calorie}=4.2\times {10}^{7}\mathrm{ergs})$ close to :