Thermodynamics PYQ — Page 16

The temperature, at which the root mean square velocity of hydrogen molecules equals their escape their escape velocity from the earth, is closest to: $[$ Boltzmann Constant ${k}_{B}=1.38\times {10}^{-23} J/K$ Avogadro number ${N}_{A}=6.02\times {10}^{26} /kg$ Radius of Earth: $6.4\times {10}^{6} m$ Gravitational acceleration on Earth $=10 m{s}^{-2}]$

A gas mixture consists of 3 moles of oxygen and 5 moles of argon at temperature T. Considering only translational and rotational modes, the total internal energy of the system is

Two rods $A$ and $B$ of identical dimensions are at temperature $30^{\circ} \mathrm{C}$. If $\mathrm{A}$ is heated upto $180^{\circ} \mathrm{C}$ and $\mathrm{B}$ upto $\mathrm{T}^{\circ} \mathrm{C},$ then the new lengths are the same. If the ratio of the coefficients of linear expansion of $\mathrm{A}$ and $\mathrm{B}$ is $4: 3,$ then the value of $T$ is

In a process, temperature and volume of one mole of an ideal monoatomic gas are varied according to the relation $\mathrm{VT}=\mathrm{K},$ where $\mathrm{K}$ is a constant. In this process the temperature of the gas is increased by $\Delta \mathrm{T}$. The amount of heat absorbed by gas is (R is gas constant):

$2\mathrm{kg}$ of a monoatomic gas is at a pressure of $4\times {10}^{4}N{m}^{-2}$. The density of the gas is $8 \mathrm{kg}{m}^{-3}$. What is the order of energy of the gas due to its thermal motion?

When $100 \mathrm{~g}$ of a liquid $\mathrm{A}$ at $100^{\circ} \mathrm{C}$ is added to $50 \mathrm{~g}$ of a liquid $B$ at temperature $75^{\circ} \mathrm{C}$, the temperature of the mixture becomes $90^{\circ} \mathrm{C}$. The temperature of the mixture, if $100 \mathrm{~g}$ of liquid $A$ at $100^{\circ} \mathrm{C}$ is added to $50 \mathrm{~g}$ of liquid $\mathrm{B}$ at $50^{\circ} \mathrm{C}$, will be:

A thermally insulated vessel contains $150 g$ of water at $0^{\circ}C$ . Then the air from the vessel is pumped out adiabatically. A fraction of water turns into ice and the rest evaporates at $0^{\circ}C$ itself. The mass of evaporated water will be closest to: (Latent heat of vaporization of water $=2.10\times {10}^{6} J k{g}^{-1}$ and Latent heat of Fusion of water $=3.36\times {10}^{5} J k{g}^{-1}$ )

A rigid diatomic ideal gas undergoes an adiabatic process at room temperature. The relation between temperature and volume for this process is $\mathrm{TV}^{\mathrm{x}}=$ constant, then $\mathrm{x}$ is:

An unknown metal of mass $192 g$ heated to a temperature of $100^{\circ}C$ was immersed into a brass calorimeter of mass $128 g$ containing $240 g$ of water at a temperature of ${8.4}^{o}C.$ Calculate the specific heat of the unknown metal if water temperature stabilizes at ${21.5}^{o}C.$ $($ Specific heat of brass is $394J k{g}^{-1}{K}^{-1})$

One mole of an ideal gas passes through a process where pressure and volume obey the relation $P={P}_{o}[1-\frac{1}{2}{(\frac{{V}_{o}}{V})}^{2}]$ . Here ${P}_{o}$ and ${V}_{o}$ are constants. Calculate the change in the temperature of the gas if its volume changes from ${V}_{o}$ to $2{V}_{o}$ .

An ideal gas occupies a volume of $2{m}^{3}$ at a pressure of $3\times {10}^{6}Pa.$ The energy of the gas is:

$1\mathrm{kg}$ of water, at $20 ^{\circ}C$ is heated in an electric kettle whose heating element has a mean (temperature averaged) resistance of $20 \Omega .$ The rms voltage in the mains is $200 V$. Ignoring heat loss from the kettle, time taken for water to evaporate fully is close to [ Specific heat of water $=4200 J{\mathrm{kg}}^{-1}^{\circ}{C}^{-1}$ Latent heat of water $=2260 kJk{g}^{-1}$ ]

$n$ moles of an ideal gas with constant volume heat capacity ${C}_{v}$ undergo an isobaric expansion by certain volume. The ratio of the work done in the process, to the heat supplied is:

A $25\times {10}^{-3} {m}^{3}$ volume cylinder is filled with $1$ mol of ${O}_{2}$ gas at room temperature $(300 K)$ . The molecular diameter of ${O}_{2}$ , and its root mean square speed, are found to be $0.3 nm$ and $200 m/s$ , respectively. What is the average collision rate (per second) for an ${O}_{2}$ molecule?

A heat source at $T={10}^{3}K$ is connected to another heat reservoir at $T={10}^{2}K$ by a copper slab which is $1 m$ thick. Given that the thermal conductivity of copper is $0.1 W{K}^{-1} {m}^{-1}$, the energy flux through it in the steady-state is:

At $40^{\circ}C,$ a brass wire of $1 mm$ radius is hung from the ceiling. A small mass, $M$ is hung from the free end of the wire. When the wire is cooled down from $40^{\circ}C$ to $20^{\circ}C$ it regains its original length of $0.2 m.$ The value of $M$ is close to: (Coefficient of linear expansion and Young’s modulus of brass are ${10}^{-5}{/}^{^{\circ}}C$ and ${10}^{11} N/{m}^{2},$ respectively; $g=10 m {s}^{-2}$ )

A uniform cylindrical rod of length $L$ and radius r, is made from a material whose Young’s modulus of Elasticity equals $Y.$ When this rod is heated by temperature T and simultaneously subjected to a net longutudinal compressional force F, its length remains unchanged. The coefficient of volume expansion, of the material of the rod, is (nearly) equal to:

The number density of molecules of a gas depends on their distance r from the origin as, $n(r)={n}_{0}{e}^{-\alpha {r}^{4}}.$ Then the numer of molecules is proportional to:

Temperature difference of ${120}^{o}C$ is maintained between two ends of a uniform rod $AB$ of length $2L.$ Another bent rod $PQ,$ of same cross-section as $AB$ and length $\frac{3L}{2},$ is connected across $AB$ (See figure). In steady state, temperature difference between $P$ and $Q$ will be close to: 

One mole of an ideal monoatomic gas is compressed isothermally in a rigid vessel to double its pressure at room temperature, $27^{\circ} \mathrm{C}$. The work done on the gas will be:

The value closest to the thermal velocity of a Helium atom at room temperature $(300 \mathrm{~K})$ in $\mathrm{ms}^{-1}$ is: $\left[\mathrm{k}_{\mathrm{B}}=1.4 \times 10^{-23} \mathrm{~J} / \mathrm{K} ; \mathrm{m}_{\mathrm{He}}=7 \times 10^{-27} \mathrm{~kg}\right]$

One mole of an ideal monatomic gas is taken along the path $ABCA$ as shown in the $PV$ diagram. The maximum temperature attained by the gas along the path $BC$ is given by: 

One mole of an ideal monatomic gas is compressed isothermally in a rigid vessel to double its pressure at room temperature, ${27}^{o}C$ . The magnitude of work done on the gas will be:

Two moles of helium are mixed with n moles of hydrogen. If $\frac{{C}_{p}}{{C}_{v}}=\frac{3}{2}$ for the mixture then the value of $n$ is,