Heat & Thermodynamics — JEE Main PYQs

Which of the following graphs represent the behaviour of an ideal gas? Symbols have their usual meaning.

One mole of an ideal gas at $27^{\circ }\mathrm{C}$ is taken from A to B as shown in the given PV indicator diagram. The work done by the system will be ____ $\times 10^{-1}\mathrm{J}$.
[Given : R = 8.3J/mole K, $\ell n2=0.6931$ ] (Round off to the nearest intege …

The height of victoria falls is 63 m. What is the difference in temperature of water at the top and at the bottom of fall ?
[Given $1\mathrm{cal}=4.2\mathrm{J}$ and specific heat of water $=1{\mathrm{calg}}^{-1}{}^{\circ }{\mathrm{C}}^{-1}$]

If the rms speed of oxygen molecules at $0^{\circ }\mathrm{C}$ is $160\mathrm{m}/\mathrm{s}$, find the rms speed of hydrogen molecules at $0^{\circ }\mathrm{C}$.

A heat engine operates between a cold reservoir at temperature $T_2=400\mathrm{K}$ and a hot reservoir at temperature ${\mathrm{T}}_1$. It takes 300 J of heat from the hot reservoir and delivers 240 J of heat to the cold reservoir in a cycle. The minimum temperature of the ho …

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 …

A diatomic gas, having $C_P=\frac{7}{2}R$ and $C_V=\frac{5}{2}R$, is heated at constant pressure. The ratio dU : dQ : dW :

In a certain thermodynamical process, the pressure of a gas depends on its volume as ${\mathrm{kV}}^3$. The work done when the temperature changes from $100^{\circ }\mathrm{C}$ to $300^{\circ }\mathrm{C}$ will be ____ nR , where n denotes numbers of moles of a gas.

A mono-atomic gas of mass $4.0u$ is kept in an insulated container. Container is moving with velocity $30\mathrm{m}/\mathrm{s}$. If container is suddenly stopped then change in temperature of the gas $(R=$ gas constant) is $\frac{x}{3R}$. Value of $x$ …

What will be the average value of energy for a monoatomic gas in thermal equilibrium at temperature T ?

In 5 minutes, a body cools from $75^{\circ }\mathrm{C}$ to $65^{\circ }\mathrm{C}$ at room temperature of $25^{\circ }\mathrm{C}$. The temperature of body at the end of next 5 minutes is ______ ${}^{\circ }\mathrm{C}$.

The temperature $\theta$ at the junction of two insulating sheets, having thermal resistances ${\mathrm{R}}_1$ and ${\mathrm{R}}_2$ as well as top and bottom temperatures ${\theta }_1$ and ${\theta }_2$ (as shown in figure) is given by :

A container is divided into two chambers by a partition . The volume of first chamber is 4.5 litre and second chamber is 5.5 litre. The first chamber contain 3.0 moles of gas at pressure 2.0 atm and second chamber contain 4.0 moles of gas at pressure 3.0 atm . After the partition …

For an ideal gas ${\mathrm{PT}}^3=$ constant. Find the coefficient of volume expansion of the gas is:

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 end A, B and D are maintained at $200^{\circ }\mathrm{C}$, $100^{\circ }\mathrm{C}$ and $125^{\circ }\mathrm{C}$ respectively. The heat current in CD is P …

The internal energy ($U$), pressure ($P$) and volume ($V$) of an ideal gas are related as $\mathrm{U}=3\mathrm{PV}+4$. The gas is:

The volume V of a given mass of monoatomic gas changes with temperature T according to the relation $\mathrm{V}={\mathrm{kT}}^{\frac{2}{3}}$. The work done when temperature changes by 90 K will be xR . The value of x is. ____
[R = universal gas constant]

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 ____ [ $\mathrm{R}=$ universal gas constant]

Two thin metallic spherical shells of radii $r_1$ and $r_2$ ($r_1<r_2$) are placed with their centres coinciding. A material of thermal conductivity K is filled in the space between the shells. The inner shell is maintained at temperature ${\theta }_1$ and the outer shell at tempe …

A mixture of hydrogen and oxygen has volume $500{\mathrm{cm}}^3$, temperature 300 K , pressure 400 kPa and mass 0.76 g . The ratio of masses of oxygen to hydrogen will be :-

A sample of gas with $\gamma =1.5$ is taken through an adiabatic process in which the volume is compressed from $1200{\mathrm{cm}}^3$ to $300{\mathrm{cm}}^3$. If the initial pressure is 200 kPa. The absolute value of the work done by the gas in the process = $\_\_\_\_$ J.

A reversible engine has an efficiency of $\frac{1}{4}$. If the temperature of the sink is reduced by $58^{\circ }\mathrm{C}$, its efficiency becomes double. Calculate the temperature of the sink :

For an ideal gas the instantaneous change in pressure ' p ' with volume ' v ' is given by the equation $\frac{\mathrm{dp}}{\mathrm{dv}}=-\mathrm{ap}$. If $\mathrm{p}={\mathrm{p}}_0$ at $\mathrm{v}=0$ is the given boundary condition, then the maximum temperature one mole of …

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

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 $\mathrm{A}\to \mathrm{B}$ and $\mathrm{C}\to \mathrm{D}$ are ${\mathrm{T}}_1$ and $T_2$ ($T_1>T_2$) respectively. …

A body takes 4 min. to cool from $61^{\circ }\mathrm{C}$ to $59^{\circ }\mathrm{C}$. If the temperature of the surroundings is $30^{\circ }\mathrm{C}$, the time taken by the body to cool from $51^{\circ }\mathrm{C}$ to $49^{\circ }\mathrm{C}$ is:

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

A Carnot's engine working between 400 K and 800 K has a work output of 1200 J per cycle. The amount of heat energy supplied to the engine from the source in each cycle is:

Two ideal polyatomic gages at temperatures $T_1$ and $T_2$ are mixed so that there is no loss of energy. If $F_1$ and $F_2,m_1$ and $m_2,n_1$ and $n_2$ be the degrees of freedom, masses, number of molecules of the first and second gas respectively, t …

Two identical metal of thermal conductivities ${\mathrm{K}}_1$ and ${\mathrm{K}}_2$ respectively are connected in series. The effective thermal conductivity of the combination is:

Two different metal bodies $A$ and $B$ of equal mass are heated at a uniform rate under similar conditions. The variation of temperature of the bodies is graphically represented as shown in the figure. The ratio of specific heat capacities is:

A monoatomic ideal gas, initially at temperature $T_1$ is enclosed in a cylinder fitted with a frictionless piston. The gas is allowed to expand adiabatically to a temperature $T_2$ by releasing the piston suddenly. If ${\ell }_1$ and ${\ell }_2$ are the lengths of the gas colu …

For a gas $C_P-C_V=R$ in a state $P$ and $C_P-C_V=1.10R$ in a state $Q$, $T_P$ and $T_Q$ are the temperatures in two different states P and Q respectively. Then

A heat engine has an efficiency of $\frac{1}{6}$. When the temperature of sink is reduced by $62^{\circ }\mathrm{C}$, its efficiency get doubled. The temperature of the source is :

A system consists of two types of gas molecules $A$ and $B$ having same number density $2\times 10^{25}/{\mathrm{m}}^3$. The diameter of A and B are $10\text{ A˚}$ and $5\text{ A˚}$ respectively. They suffer collision at room temperature. The ratio of average distance covered by t …

One mole of an ideal gas is taken through an adiabatic process where the temperature rises from $27^{\circ }\mathrm{C}$ to $37^{\circ }\mathrm{C}$. If the ideal gas is composed of polyatomic molecule that has 4 vibrational modes, which of the following of the following is true? …

Two Carnot engines $A$ and operate in series such that engine $A$ absorbs heat at $T_1$ and rejects heat to a sink at temperature T. Engine B absorbs half of the heat rejected by Engine A and rejects heat to the sink at $T_3$. When work done in both the cases is equal, the va …

Due to cold weather a 1 m water pipe of cross-sectional area $1{\mathrm{cm}}^2$ is filled with ice at $-10^{\circ }\mathrm{C}$. Resistive heating is used to melt the ice. Current of 0.5 A is passed through $4\mathrm{k}\Omega$ resistance. Assuming that all the heat produced is …

A steel rod with $\mathrm{y}=2.0\times 10^{11}{\mathrm{Nm}}^{-2}$ and $\alpha =10^{-5}{}^{\circ }{\mathrm{C}}^{-1}$ of length 4 m and area of cross-section 10 ${\mathrm{cm}}^2$ is heated from $0^{\circ }\mathrm{C}$ to $400^{\circ }\mathrm{C}$ without being allowed to extend. The te …

The temperature of 3.00 mol of an ideal diatomic gas is increased by $40.0^{\circ }\mathrm{C}$ without changing the pressure of the gas. The molecules in the gas rotate but do not oscillate. If the ratio of change in internal energy of the gas to the amount of work done by the ga …

The average translational kinetic energy of ${\mathrm{N}}_2$ gas molecules at ______ ${}^{\circ }\mathrm{C}$ becomes equal to the K.E. of an electron accelerated from rest through a potential difference of 0.1 volt. (Given …

The volume V of an enclosure contains a mixture of three gases, 16 g of oxygen, 28 g of nitrogen and 44 g of carbon dioxide at absolute temperature T . Consider R as universal gas constant. The pressure of the mixture of gases is :

In thermodynamics, heat and work are :

Calculate the value of mean free path ($\lambda$) for oxygen molecules at temperature $27^{\circ }\mathrm{C}$ and pressure $1.01\times 10^5\mathrm{Pa}$. Assume the molecular diameter 0.3 nm and the gas is ideal. $(\mathrm{k}=1.38\times 10^{-23}{\mathrm{JK}}^{-1})$

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 metal B . When bimetallic strip is placed in a cold bath, it will

For an ideal heat engine, the temperature of the source is $127^{\circ }\mathrm{C}$. In order to have $60\%$ efficiency the temperature of the sink should be ⋯⋯----- ${}^{\circ }\mathrm{C}$. (Round off to the Nearest Integer)

For an adiabatic expansion of an ideal gas , the fractional change in its pressure is equal to ( where $\gamma$ is the ratio of specific heats):

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 :

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

If one mole of the polyatomic gas is having two vibrational modes and $\beta$ is the ratio of molar specific heats for polyatomic gas $\left(\beta =\frac{C_P}{C_V}\right)$ then the value of $\beta$ is: