Thermodynamics PYQ — Page 11

A bimetallic strip consists of metals $A$ and $B$. It is mounted rigidly as shown. The metal $A$ has higher coefficient of expansion compared to that of metal $B$. When the bimetallic strip is placed in a cold both, it will : 

Each side of a box made of metal sheet in cubic shape is $a$ at room temperature $T$, the coefficient of linear expansion of the metal sheet is $\alpha$. The metal sheet is heated uniformly, by a small temperature $\Delta T$, so that its new temperature is $T+\Delta T$. Calculate the increase in the volume of the metal box.

One mole of an ideal gas is taken through an adiabatic process where the temperature rises from $27^{\circ}C$ to $37^{\circ}C$. If the ideal gas is composed of polyatomic molecule that has 4 vibrational modes, which of the following is true? $[R=8.314J{\mathrm{mol}}^{-1}{k}^{-1}]$

Two spherical soap bubbles of radii ${r}_{1}$ and ${r}_{2}$ in vacuum combine under isothermal conditions. The resulting bubble has a radius equal to:

A rod $CD$ of thermal resistance $10.0{\mathrm{KW}}^{-1}$ is joined at the middle of an identical rod $AB$ as shown in figure. The ends $A,B$ and $D$ are maintained at $200^{\circ}C,100^{\circ}C$ and $125^{\circ}C$ respectively. The heat current in $CD$ is $PW$. The value of $P$ is 

$1$ mole of rigid diatomic gas performs a work of $\frac{Q}{5}$ when heat $Q$ is supplied to it. The molar heat capacity of the gas during this transformation is $\frac{xR}{8}.$ The value of $x$ is [$R$ universal gas constant]

The number of molecules in one litre of an ideal gas at $300K$ and $2$ atmospheric pressure with mean kinetic energy $2\times {10}^{-9}J$ per molecule is:

In the reported figure, heat energy absorbed by a system in going through a cyclic process is ______$\pi J.$ 

Consider a sample of oxygen behaving like an ideal gas. At $300K$, the ratio of root-mean-square (RMS) velocity to the average velocity of the gas molecule would be : (Molecular weight of oxygen is $32g{\mathrm{mol}}^{-1};R=8.3J{K}^{-1}{\mathrm{mol}}^{-1}$)

Given below are two statements: one is labelled as Assertion $A$ and the other is labelled as Reason $R$. Assertion $A$ : When a rod lying freely is heated, no thermal stress is developed in it. Reason $R$ : On heating, the length of the rod increases. In the light of the above statements, choose the correct answer from the options given below:

For an ideal gas the instantaneous change in pressure $P$ with volume $V$ is given by the equation $\frac{dP}{dV}=-aP.$ If $P={P}_{0}$ at $V=0$ is the given boundary condition, then the maximum temperature one mole of gas can attain is: (Here $R$ is the gas constant)

The temperature $\theta$ at the junction of two insulating sheets, having thermal resistances ${R}_{1}$ and ${R}_{2}$ as well as top and bottom temperatures ${\theta }_{1}$ and ${\theta }_{2}$ (as shown in figure) is given by : 

A $2\mathrm{kg}$ steel rod of length $0.6m$ is clamped on a table vertically at its lower end and is free to rotate in the vertical plane. The upper end is pushed so that the rod falls under gravity. Ignoring the friction due to clamping at its lower end, the speed of the free end of the rod when it passes through its lowest position is $_______m{s}^{-1}.$ (Take $g=10{ms}^{-2})$

In the reported figure, there is a cyclic process $ABCDA$ on a sample of $1$ mol of a diatomic gas. The temperature of the gas during the process $A\rightarrow B$ and $C\rightarrow D$ are ${T}_{1}$ and ${T}_{2}({T}_{1}>{T}_{2})$ respectively.  Choose the correct option out of the following for work done if processes $BC$ and $DA$ are adiabatic.

An ideal gas in a cylinder is separated by a piston in such a way that the entropy of one part is ${S}_{1}$ and that of the other part is ${S}_{2}$. Given that ${S}_{1}>{S}_{2}$. If the piston is removed then the total entropy of the system will be:

A Carnot engine operates between temperatures 600 K and 300 K...

In thermodynamics, heat and work are :

The width of one of the two slits in a Young's double slit experiment is three times the other slit. If the amplitude of the light coming from a slit is proportional to the slit-width, the ratio of minimum to maximum intensity in the interference pattern is $x:4$ where $x$ is $_______.$

If the R.M.S. speed of oxygen molecules at $0^{\circ}C$ is $160m{s}^{-1}$. Find the R.M.S. speed of hydrogen molecules at $0^{\circ}C$.

A system consists of two types of gas molecules $A$ and $B$ having the same number density $2\times {10}^{25}{m}^{-3}$. The diameter of $A$ and $B$ are $10A$ and $5A$ respectively. They suffer collisions at room temperature. The ratio of average distance covered by the molecule $A$ to that of $B$ between two successive collisions is ___________$\times {10}^{-2}$

The R.M.S. speeds of the molecules of Hydrogen, Oxygen, and Carbon dioxide at the same temperature are ${v}_{H},{v}_{O}$ and ${v}_{C}$ respectively, then:

Two identical metal wires of thermal conductivities ${K}_{1}$ and ${K}_{2}$ respectively are connected in series. The effective thermal conductivity of the combination is:

A polyatomic ideal gas has $24$ vibrational modes. What is the value of $\gamma ?$

Thermodynamic process is shown below on a $P-V$ diagram for one mole of an ideal gas. If ${V}_{2}=2{V}_{1}$, then the ratio of temperature $\frac{{T}_{2}}{{T}_{1}}$ is :