Heat & Thermodynamics — JEE Main PYQs

A poly-atomic molecule ( ${\mathrm{C}}_{\mathrm{V}}=3\mathrm{R},{\mathrm{C}}_{\mathrm{P}}=4\mathrm{R}$, where $R$ is gas constant) goes from phase space point …

A cup of coffee cools from $90^{\circ }\mathrm{C}$ to $80^{\circ }\mathrm{C}$ in t minutes when the room temperature is $20^{\circ }\mathrm{C}$. The time taken by the similar cup of coffee to cool from $80^{\circ }\mathrm{C}$ to $60^{\circ }\mathrm{C}$ at the same room temperatur …

The workdone in an adiabatic change in an ideal gas depends upon only :

A container of fixed volume contains a gas at $27^{\circ }\mathrm{C}$. To double the pressure of the gas, the temperature of gas should be raised to $\_\_\_\_$ ${}^{\circ }\mathrm{C}$.

The ratio of vapour densities of two gases at the same temperature is $\frac{4}{25}$, then the ratio of r.m.s. velocities will be :

The kinetic energy of translation of the molecules in 50 g of ${\mathrm{CO}}_2$ gas at $17^{\circ }\mathrm{C}$ is :

A Carnot engine (E) is working between two temperatures 473 K and 273 K. In a new system two engines - engine ${\mathrm{E}}_1$ works between 473 K to 373 K and engine ${\mathrm{E}}_2$ works between 373 K to 273 K. If ${\eta }_{12}$, ${\eta }_1$ and ${\eta }_2$ are the efficiencies of …

For a particular ideal gas which of the following graphs represents the variation of mean squared velocity of the gas molecules with temperature?

Given below are two statements. One is labelled as Assertion (A) and the other is labelled as Reason(R).
Assertion (A) : In an insulated container, a gas is adiabatically shrunk to half of its initial volume. The temperature of the gas decreases.
Reason (R) : Free expansion of an …

The magnitude of heat exchanged by a system for the given cyclic process ABCA (as shown in figure) is (in SI unit)

The temperature of a body in air falls from $40^{\circ }\mathrm{C}$ to $24^{\circ }\mathrm{C}$ in 4 minutes. The temperature of the air is $16^{\circ }\mathrm{C}$. The temperature of the body in the next 4 minutes will be :

An ideal gas goes from an initial state to final state.
During the process, the pressure of gas increases linearly with temperature.
A. The work done by gas during the process is zero.
B. The heat added to gas is different from change in its internal energy.
C. The volume of the …

The temperature of 1 mole of an ideal monoatomic gas is increased by $50^{\circ }\mathrm{C}$ at constant pressure. The total heat added and change in internal energy are ${\mathrm{E}}_1$ and ${\mathrm{E}}_2$, respectively. If …

Identify the characteristics of an adiabatic process in a monoatomic gas.
(A) Internal energy is constant.
(B) Work done in the process is equal to the change in internal energy.
(C) The product of temperature and volume is a constant.
(D) The product of pressure and volume is a …

Match List-I with List-II.

List-I
(A) Heat capacity of body
(B) Specific heat capacity of body
(C) Latent heat
(D) Thermal conductivity

List-II
(I) $\mathrm{J}{\mathrm{kg}}^{-1}$
(II) ${\mathrm{JK}}^{-1}$
(III) $\mathrm{J}{\mathrm{kg}}^{-1}{\mathrm{K}}^{-1}$
(IV) …

The internal energy of air in $4\mathrm{m}\times 4\mathrm{m}\times 3\mathrm{m}$ sized room at 1 atmospheric pressure will be ______ $\times 10^6\mathrm{J}$.
(Consider air as diatomic molecule)

During the melting of a slab of ice at 273 K at atmospheric pressure :

A piston of mass M is hung from a massless spring whose restoring force law goes as $\mathrm{F}=-{\mathrm{kx}}^3$, where k is the spring constant of appropriate dimension. The piston separates the vertical chamber into two parts, where the bottom part is filled with ' n ' moles o …

A gas is kept in a container having walls which are thermally non-conducting. Initially the gas has a volume of $800{\mathrm{cm}}^3$ and temperature $27^{\circ }\mathrm{C}$. The change in temperature when the gas is adiabatically compressed to $200{\mathrm{cm}}^3$ is :
(Take …

An ideal gas exists in a state with pressure ${\mathrm{P}}_0$, volume ${\mathrm{V}}_0$. It is isothermally expanded to 4 times of its initial volume (${\mathrm{V}}_0$), then isobarically compressed to its original volume. Finally the system is heated isochorically to bring …

Pressure of an ideal gas, contained in a closed vessel, is increased by $0.4\%$ when heated by $1^{\circ }\text{C}$. Its initial temperature must be:

The mean free path and the average speed of oxygen molecules at 300 K and 1 atm are $3\times 10^{-7}\mathrm{m}$ and $600\mathrm{m}/\mathrm{s}$, respectively. Find the frequency of its collisions.

The helium and argon are put in the flask at the same room temperature ( 300 K ). The ratio of average kinetic energies (per molecule) of helium and argon is :
(Give : Molar mass of helium $=4\mathrm{g}/\mathrm{mol}$, Molar mass of argon $=40\mathrm{g}/\mathrm{mol}$ )

Two cylindrical rods A and B made of different materials, are joined in a straight line. The ratio of lengths, radii and thermal conductivities of these rods are : …

A wire of length 10 cm and diameter 0.5 mm is used in a bulb. The temperature of the wire is $1727^{\circ }$C and power radiated by the wire is 94.2 W. Its emissivity is $\frac{X}{8}$ where $x=$ ____ (Given $\sigma =6.0\times 10^{-8}$ W m${}^{-2}$ K${}^{-4}$, $\pi =3.14$ and assume that …

An ideal gas has undergone through the cyclic process as shown in the figure. Work done by the gas in the entire cycle is ______ $\times 10^{-1}$ J.
(Take $\pi =3.14$)

Water falls from a height of 200 m into a pool. Calculate the rise in temperature of the water assuming no heat dissipation from the water in the pool.
(Take $\mathrm{g}=10\mathrm{m}/{\mathrm{s}}^2$, specific heat of water $=4200\mathrm{J}/(\mathrm{kg}\mathrm{K})$)

A monoatomic gas having $\gamma =\frac{5}{3}$ is stored in a thermally insulated container and the gas is suddenly compressed to ${\left(\frac{1}{8}\right)}^{\text{th }}$ of its initial volume. The ratio of final pressure and initial pressure is: ($\gamma$ is the ratio of spe …

Consider a rectangular sheet of solid material of length $\ell =9\mathrm{cm}$ and width $\mathrm{d}=4\mathrm{cm}$. The coefficient of linear expansion is $\alpha =3.1\times 10^{-5}{\mathrm{K}}^{-1}$ at room temperature and one atmospheric pressure. The mass of sheet …

There are two vessels filled with an ideal gas where volume of one is double the volume of other. The large vessel contains the gas at 8 kPa at 1000 K while the smaller vessel contains the gas at 7 kPa at 500 K . If the vessels are connected to each other by a thin tube allowing …

${\gamma }_{\mathrm{A}}$ is the specific heat ratio of monoatomic gas A having 3 translational degrees of freedom. ${\gamma }_{\mathrm{B}}$ is the specific heat ratio of polyatomic gas B having 3 translational, 3 rotational degrees of freedom and 1 vibrational mode. If …

Which of the following figure represents the relation between Celsius (C) and Fahrenheit (F) temperatures? [graph options in source]

Match List-I with List-II:
List-I: (A) Isothermal (B) Adiabatic (C) Isobaric (D) Isochoric
List-II: (I) W (work done) = 0 (II) Q (supplied heat) = 0 (III) ΔU (change in internal energy) ≠ 0 (IV) ΔU = 0
Choose the correct answer from the options given below:

Energy of 10 non rigid diatomic molecules at temperature T is :

A total of 48J heat is given to one mole of helium kept in a cylinder. The temperature of helium increases by $2^{\circ }\mathrm{C}$. The work done by the gas is :\\
Given, $\mathrm{R}=8.3{\mathrm{JK}}^{-1}{\mathrm{mol}}^{-1}$.

The translational degrees of freedom ($f_t$) and rotational degrees of freedom $\left({\mathrm{f}}_{\mathrm{r}}\right)$ of ${\mathrm{CH}}_4$ molecule are :

A sample of gas at temperature T is adiabatically expanded to double its volume. Adiabatic constant for the gas is $\gamma =3/2$. The work done by the gas in the process is : ( $\mu =1$ mole)

On celcius scale the temperature of body increases by $40^{\circ }\mathrm{C}$. The increase in temperature on Fahrenheit scale is:

P-T diagram of an ideal gas having three different densities ${\rho }_1,{\rho }_2,{\rho }_3$ (in three different cases) is shown in the figure. Which of the following is correct :

If n is the number density and d is the diameter of the molecule, then the average distance covered by a molecule between two successive collisions (i.e. mean free path) is represented by :

During an adiabatic process, if the pressure of a gas is found to be proportional to the cube of its absolute temperature, then the ratio of $\frac{C_P}{C_V}$ for the gas is :

If the collision frequency of hydrogen molecules in a closed chamber at $27^{\circ }\mathrm{C}$ is Z , then the collision frequency of the same system at $127^{\circ }\mathrm{C}$ is :

The heat absorbed by a system in going through the given cyclic process is :

The specific heat at constant pressure of a real gas obeying ${\mathrm{PV}}^2=\mathrm{RT}$ equation is:

A sample contains mixture of helium and oxygen gas. The ratio of root mean square speed of helium and oxygen in the sample, is :

A mixture of one mole of monoatomic gas and one mole of a diatomic gas (rigid) are kept at room temperature $\left(27^{\circ }\mathrm{C}\right)$. The ratio of specific heat of gases at constant volume respectively is:

Two different adiabatic paths for the same gas intersect two isothermal curves as shown in P-V diagram. The relation between the ratio $\frac{{\mathrm{V}}_{\mathrm{a}}}{{\mathrm{V}}_{\mathrm{d}}}$ and the ratio $\frac{V_b}{V_c}$ is:

Given below are two statements :

Statement (I) : The mean free path of gas molecules is inversely proportional to square of molecular diameter.

Statement (II) : Average kinetic energy of gas molecules is directly proportional to absolute temperature of gas.
In the light of the …

A diatomic gas $(\gamma =1.4)$ does 100 J of work in an isobaric expansion. The heat given to the gas is :

The volume of an ideal gas $(\gamma =1.5)$ is changed adiabatically from 5 litres to 4 litres. The ratio of initial pressure to final pressure is: