Heat & Thermodynamics — JEE Main PYQs

A cylindrical tube $AB$ of length $l$, closed at both ends contains an ideal gas of 1 mol having molecular weight $M$. The tube is rotated in a horizontal plane with constant angular velocity $\omega$ about an axis perpendicular to $AB$ and passing through the edge at end A, as s …

Rods $x$ and $y$ of equal dimensions but of different materials are joined as shown in figure. Temperatures of end points $A$ and $F$ are maintained at $100^{\circ }\mathrm{C}$ and $40^{\circ }\mathrm{C}$ respectively. Given the thermal conductivity of rod x is three …

The volume of an ideal gas increases 8 times and temperature becomes $(1/4{)}^{\text{th }}$ of initial temperature during a reversible change. If there is no exchange of heat in this process ( $\Delta \mathrm{Q}=0$ ) then identify the gas from the following options (Assuming …

Consider two boxes containing ideal gases A and B such that their temperatures, pressures and number densities are same. The molecular size of A is half of that of B and mass of molecule A is four times that of B. If the collision frequency in gas B is …

An insulated cylinder of volume $60{\mathrm{cm}}^3$ is filled with a gas at $27^{\circ }\mathrm{C}$ and 2 atmospheric pressure. Then the gas is compressed making the final volume as $20{\mathrm{cm}}^3$ while allowing the temperature to rise to $77^{\circ }\mathrm{C}$. The fin …

The r.m.s speed of oxygen molecules at $47^{\circ }\mathrm{C}$ is equal to that of the hydrogen molecules kept at $\_\_\_\_$ ${}^{\circ }\mathrm{C}$. (Mass of oxygen molecule/mass of hydrogen molecule=32/2)

A diatomic gas $(\gamma =1.4)$ does 100 J of work when it is expanded isobarically. Then the heat given to the gas ______ J.

The internal energy of a monoatomic gas is 3 nRT. One mole of helium is kept in a cylinder having internal cross section area of $17{\mathrm{cm}}^2$ and fitted with a light movable frictionless piston. The gas is heated slowly by suppling 126 J heat. If the temperature rises …

An air bubble of volume $2.9{\mathrm{cm}}^3$ rises from the bottom of a swimming pool of 5 m deep. At the bottom of the pool water temperature is $17^{\circ }\mathrm{C}$. The volume of the bubble when it reaches the surface, where the water temperature is …

One mole of an ideal diatomic gas expands from volume V to 2V isothermally at a temperature $27^{\circ }\mathrm{C}$ and does W joule of work. If the gas undergoes same magnitude of expansion adiabatically from $27^{\circ }\mathrm{C}$ doing the same amount of work W, then its final …

Density of water at $4^{\circ }\mathrm{C}$ and $20^{\circ }\mathrm{C}$ are $1000\mathrm{kg}/{\mathrm{m}}^3$ and $998\mathrm{kg}/{\mathrm{m}}^3$ respectively. The increase in internal energy of 4 kg water when it is heated from $4^{\circ }\mathrm{C}$ to …

A brass wire of length 2 m and radius 1 mm at $27^{\circ }\mathrm{C}$ is held taut between two rigid supports. Initially it was cooled to a temperature of $-43^{\circ }\mathrm{C}$ creating a tension T in the wire. The temperature to which the wire has to be cooled in order to inc …

A gas of certain mass filled in a closed cylinder at a pressure of 3.23 kPa has temperature $50^{\circ }\mathrm{C}$. The gas is now heated to double its temperature. The modified pressure is ______ Pa.

10 kg of ice at $-10^{\circ }\mathrm{C}$ is added to 100 kg of water to lower its temperature from $25^{\circ }\mathrm{C}$. Consider no heat exchange to surroundings. The decrement to the temperature of water is ______ ${}^{\circ }\mathrm{C}$.
(specific heat of ice …

Which of the following best represents the temperature versus heat supplied graph for water, in the range of $-20^{\circ }\mathrm{C}$ to $120^{\circ }\mathrm{C}$?

In the following $p-V$ diagram the equation of state along the curved path is given by $(V-2{)}^2=4ap$ where $a$ is a constant. The total work done in the closed path is

10 mole of an ideal gas is undergoing the process shown in the figure. The heat involved in the process from ${\mathrm{P}}_1$ to ${\mathrm{P}}_2$ is $\alpha$ Joule $({\mathrm{P}}_1=21.7\mathrm{Pa}$ and …

The mean free path of a molecule of diameter $5\times 10^{-10}\mathrm{m}$ at the temperature $41^{\circ }\mathrm{C}$ and pressure $1.38\times 10^5\mathrm{Pa}$, is given as ______ m.
(Given ${\mathrm{k}}_{\mathrm{B}}=1.38\times 10^{-23}\mathrm{J}/\mathrm{K}$ ).

A thermodynamic system is taken through the cyclic process ABC as shown in the figure. The total work done by the system during the cycle ABC is ______ J.

A gas based geyser heats water flowing at the rate of 5.0 litres per minute from $27^{\circ }\mathrm{C}$ to $87^{\circ }\mathrm{C}$.
The rate of consumption of the gas is ____ g/s.
(Take heat of combustion of gas $=5.0\times 10^4\mathrm{J}/\mathrm{g}$) specific h …

An aluminium and steel rods having same lengths and cross-sections are joined to make total length of 120 cm at $30^{\circ }\mathrm{C}$. The coefficient of linear expansion of aluminium and steel are $24\times 10^{-6}/{}^{\circ }\mathrm{C}$ and …

10 mole of oxygen is heated at constant volume from $30^{\circ }\mathrm{C}$ to $40^{\circ }\mathrm{C}$. The change in the internal energy of the gas is ______ cal. (The molecular specific heat of oxygen at constant pressure, …

A mixture of carbon dioxide and oxygen has volume $8310{\mathrm{cm}}^3$, temperature 300 K, pressure 100 kPa and mass 13.2 g. The number of moles of carbon dioxide and oxygen gases in the mixture respectively are ____.
(Assume both carbondioxide and oxygen gases behave like i …

5 moles of unknown gas is heated at constant volume from $10^{\circ }\mathrm{C}$ to $20^{\circ }\mathrm{C}$. The molar specific heat of this gas at constant pressure ${\mathrm{c}}_{\mathrm{p}}=8\mathrm{cal}/\mathrm{mol}{.}^{\circ }\mathrm{C}$ and …

One gas of $n_1$ mole of molecules at temperature $T_1$, volume $V_1$, and pressure $P_1$, and another gas of $n_2$ mole of molecules at temperature $T_2$, volume $V_2$, and pressure $P_2$, are mixed resulting in pressure P and volume V of the mixture. The tempera …

An ideal gas undergoes a process maintaining relation between pressure (P) and volume (V) as $P=P_o{\left(1+{\left(\frac{V_o}{V}\right)}^2\right)}^{-1}$, where $P_o$ and $V_o$ are constants. If two samples A and B (two moles each) with initial volume $V_o$ and $3V_o$ …

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R

Assertion A: If the average kinetic energy of ${\mathrm{H}}_2$ and ${\mathrm{O}}_2$ molecules, kept in two different sized containers are same, then their temperatures will be sa …

The temperature of a metal strip having coefficient of linear expansion $\alpha$ is increased from ${\mathrm{T}}_1$ to ${\mathrm{T}}_2$ resulting in increase of its length by $\Delta {\mathrm{L}}_1$. The temperature is further increased from ${\mathrm{T}}_2$ to ${\mathrm{T}}_3$ s …

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R

Statement I: Change in internal energy of a system containing $n$ mole of ideal gas can be written as …

Consider the following statements:

A. Zeroth law of thermodynamics gives concept of temperature

B. First law of thermodynamics gives concept of internal energy

C. In isothermal expansion of ideal gas, $\Delta \mathrm{Q}\ne \Delta \mathrm{W}$

D. Product of intensive and exte …

An ideal gas at pressure $P$ and temperature $T$ is expanding such that $P{T}^3=$ constant. The coefficient of volume expansion of the gas is ______.

The heat extracted out of x gram of water initially at $50^{\circ }\mathrm{C}$ to cool it down to $0^{\circ }\mathrm{C}$ is sufficient to evaporate ($1000-\mathrm{x}$) gram of water also initially at $50^{\circ }\mathrm{C}$. The value of x (closest integer) is ______. (Ta …

Two closed vessels of same volume are joined through a narrow tube and both vessels are filled with air of pressure 90 kPa and temperature 400 K. Keeping the temperature of one vessel constant at 400 K the second vessel temperature is raised to 500 K. The final pressure in the ve …

A certain gas is isothermally compressed to ${\left(\frac{1}{3}\right)}^{\text{rd}}$ of its initial volume ($V_0=3$ litre) by applying required pressure. If the bulk modulus of the gas is $3\times 10^5\mathrm{N}/{\mathrm{m}}^2$, the magnitude of work done on the gas is ___ …

A cylinder with adiabatic walls is closed at both ends and is divided into two compartments by a frictionless adiabatic piston. Ideal gas is filled in both (left and right) the compartments at same $P,V,T$. Heating is started from left side until pressure changes to …

If 2 mole of an ideal monoatomic gas at temperature T, is mixed with 6 mole of another ideal monoatomic gas at temperature 2T then the temperature of mixture is:

One mole of diatomic gas having rotational modes only is kept is a cylinder with a piston system. The cross-section area of the cylinder is $4{\mathrm{cm}}^2$. The gas is heated slowly to raise the temperature by $1.2{}^{\circ }\mathrm{C}$ during which the piston moves by …

Initial pressure and volume of a monoatomic ideal gas are P and V. The change in internal energy of this gas in adiabatic expansion to volume ${\mathrm{V}}_{\text{final }}=27\mathrm{V}$ is ____ J.

Heat is supplied to a diatomic gas at constant pressure. Then the ratio of $\Delta Q:\Delta U:\Delta W$ is ____.

A vessel contains $0.15{\mathrm{m}}^3$ of a gas at pressure 8 bar and temperature $140^{\circ }\mathrm{C}$ with ${\mathrm{c}}_{\mathrm{p}}=3\mathrm{R}$ and ${\mathrm{c}}_{\mathrm{v}}=2\mathrm{R}$. It is expanded adiabatically till pressure falls to 1 bar. The work done during thi …

Two spherical bodies of same materials having radii 0.2 m and 0.8 m are placed in same atmosphere. The temperature of the smaller body is 800 K and temperature of bigger body is 400 K. If the energy radiate from the smaller body is E, the energy radiated from the bigger body is ( …

An amount of ice of mass $10^{-3}\mathrm{kg}$ and temperature $-10^{\circ }\mathrm{C}$ is transformed to vapour of temperature $110^{\circ }$ by applying heat. The total amount of work required for this conversion is, (Take, specific heat of ice …

Three conductors of same length having thermal conductivity ${\mathrm{k}}_1$, ${\mathrm{k}}_2$ and ${\mathrm{k}}_3$ are connected as shown in figure.
| $1.{\mathrm{k}}_1$ | | …

For a diatomic gas, if ${\gamma }_1=\left(\frac{\mathrm{Cp}}{\mathrm{Cv}}\right)$ for rigid molecules and ${\gamma }_2=\left(\frac{\mathrm{Cp}}{\mathrm{Cv}}\right)$ for another diatomic molecules, but also having vibrational modes. Then, which one of the following options is correc …

Given are statements for certain thermodynamic variables,
(A) Internal energy, volume (V) and mass (M) are extensive variables.
(B) Pressure (P), temperature (T) and density ( $\rho$ ) are intensive variables.
(C) Volume (V), temperature (T) and density ( $\rho$ ) are intensive v …

A gun fires a lead bullet of temperature 300 K into a wooden block. The bullet having melting temperature of 600 K penetrates into the block and melts down. If the total heat required for the process is 625 J , then the mass of the bullet is $\_\_\_\_$ grams.
(Latent heat of fusi …

An ideal gas initially at $0^{\circ }\mathrm{C}$ temperature, is compressed suddenly to one fourth of its volume. If the ratio of specific heat at constant pressure to that at constant volume is $3/2$, the change in temperature due to the thermodynamics process is $\_\_\_\_$ K.

Water of mass $m$ gram is slowly heated to increase the temperature from $T_1$ to $T_2$. The change in entropy of the water, given specific heat of water is $1{\mathrm{Jkg}}^{-1}{\mathrm{K}}^{-1}$, is :

Using the given $P-V$ diagram, the work done by an ideal gas along the path ABCD is-

Given below are two statements. One is labelled as Assertion (A) and the other is labelled as Reason (R).

Assertion (A) : With the increase in the pressure of an ideal gas, the volume falls off more rapidly in an isothermal process in comparison to the adiabatic process.

Reason …