Heat & Thermodynamics — JEE Advanced PYQs

A quasi-static cycle of a monoatomic ideal gas contains an isothermal process $(\mathbf{a}\mathbf{b})$, followed by an isochoric process $(\mathbf{b}\mathbf{c})$ and an adiabatic process $(\mathbf{c}\mathbf{a})$ as shown in the figure. The volumes of th …

As shown in the figure, five Carnot engines, each with efficiency $\eta$ and same number of cycles per unit time, are operating between six heat reservoirs. The amount of heat released per cycle by one engine is completely absorbed by the next engine. Consider ${\mathrm{Q}}_0$ to …

As shown in the figure, an insulated container is fitted with a thermally conducting but immovable partition $\left(P_1\right)$ and a freely movable but thermally insulated piston $\left(P_2\right)$. The partition $P_1$ with thermal conductivity $K$, cross sectional area A …

Ten moles of an ideal monoatomic gas, initially in state $\mathbf{a}$ at atmospheric pressure and temperature $T_a=27^{\circ }\mathrm{C}$, is enclosed in a metal cylinder of volume $V_0$ fitted with a frictionless piston. The gas is suddenly compressed to state …

Two identical plates P and Q, radiating as perfect black bodies, are kept in vacuum at constant absolute temperatures ${\mathrm{T}}_{\mathrm{P}}$ and ${\mathrm{T}}_{\mathrm{Q}}$, respectively, with ${\mathrm{T}}_{\mathrm{Q}}<{\mathrm{T}}_{\mathrm{P}}$, as shown in Fig. 1. The radia …

The efficiency of a Carnot engine operating with a hot reservoir kept at a temperature of 1000 K is 0.4. It extracts 150 J of heat per cycle from the hot reservoir. The work extracted from this engine is being fully used to run a heat pump which has a coefficient of performance 1 …

An ideal monatomic gas of n moles is taken through a cycle $WXYZW$ consisting of consecutive adiabatic and isobaric quasi-static processes, as shown in the schematic $V-T$ diagram. The volume of the gas at $W,X$ and $Y$ points are, 64 cm³, 125 cm³ and 250 cm³, respective …

The left and right compartments of a thermally isolated container of length $L$ are separated by a thermally conducting, movable piston of area $A$. The left and right compartments are filled with $\frac{3}{2}$ and 1 moles of an ideal gas, respectively. In the left compartm …

The specific heat capacity of a substance is temperature dependent and is given by the formula $C=kT$, where $k$ is a constant of suitable dimensions in SI units, and $T$ is the absolute temperature. If the heat required to raise the temperature of 1 kg of the substance fr …

One mole of a monatomic ideal gas undergoes the cyclic process $\mathrm{J}\to \mathrm{K}\to \mathrm{L}\to \mathrm{M}\to \mathrm{J}$, as shown in the P-T diagram.

Match the quantities mentioned in List-I with their values in List-II and choos …

One mole of an ideal gas expands adiabatically from an initial state ($T_{\mathrm{A}},V_0$) to final state ($T_{\mathrm{f}},5V_0$). Another mole of the same gas expands isothermally from a different initial state ($T_{\mathrm{B}},{\mathrm{V}}_0$) to the same final state ( …

A closed container contains a homogeneous mixture of two moles of an ideal monatomic gas $(\gamma =5/3)$ and one mole of an ideal diatomic gas $(\gamma =7/5)$. Here, $\gamma$ is the ratio of the specific heats at constant pressure and constant volume of an ideal gas. The gas mi …

Match the temperature of a black body given in List-I with an appropriate statement in List-II, and choose the correct option.
[Given: Wien's constant as $2.9\times 10^{-3}\mathrm{m}-\mathrm{K}$ and $\frac{\mathrm{hc}}{\mathrm{e}}=1.24\times 10^{-6}\mathrm{V}-\mathrm{m}$] …

An ideal gas is in thermodynamic equilibrium. The number of degrees of freedom of a molecule of the gas in $n$. The internal energy of one mole of the gas is $U_n$ and the speed of sound in the gas is $v_n$. At a fixed temperature and pressure, which of the following is the c …

One mole of an ideal gas undergoes two different cyclic processes I and II, as shown in the $P-V$ diagrams below. In cycle I, processes $a,b,c$ and $d$ are isobaric, isothermal, isobaric and isochoric, respectively. In cycle II, processes $a^{\prime },b^{\prime },c^{\prime }$ an …

List I describes thermodynamic processes in four different systems. List II gives the magnitudes (either exactly or as a close approximation) of possible changes in the internal energy of the system due to the process.
| (I) | …

In the given $P-V$ diagram, a monoatomic gas $\left(\gamma =\frac{5}{3}\right)$ is first compressed adiabatically from state $A$ to state $B$. Then it expands isothermally from state $B$ to state $C$. [Given: …

A thermally insulating cylinder has a thermally insulating and frictionless movable partition in the middle, as shown in the figure below. On each side of the partition, there is one mole of an ideal gas, with specific heat at constant volume, $C_v=2R$. Here, $R$ is the ga …

A thermally insulating cylinder has a thermally insulating and frictionless movable partition in the middle, as shown in the figure below. On each side of the partition, there is one mole of an ideal gas, with specific heat at constant volume, $C_v=2R$. Here, $R$ is the ga …

An ideal gas undergoes a four step cycle as shown in the $P-V$ diagram below. During this cycle, heat is absorbed by the gas in

A small object is placed at the center of a large evacuated hollow spherical container. Assume that the container is maintained at 0 K. At time $\mathrm{t}=0$, the temperature of the object is 200 K. The temperature of the object becomes 100 K at $\mathrm{t}={\mathrm{t}}_1$ and 5 …

The filament of a light bulb has surface area $64{\mathrm{mm}}^2$. The filament can be considered as a black body at temperature 2500 K emitting radiation like a point source when viewed from far. At night the light bulb is observed from a distance of 100 m. Assume the pupil of …

Consider one mole of helium gas enclosed in a container at initial pressure $P_1$ and volume $V_1$. It expands isothermally to volume $4V_1$. After this, the gas expands adiabatically and its volume becomes $32V_1$. The work done by the gas during isothermal and adiabat …

A thermally isolated cylindrical closed vessel of height 8 m is kept vertically. It is divided into two equal parts by a diathermic (perfect thermal conductor) frictionless partition of mass 8.3 kg. Thus the partition is held initially at a distance of 4 m from the top, as shown …

A container with 1 kg of water in it is kept in sunlight, which causes the water to get warmer than the surroundings. The average energy per unit time per unit area received due to the sunlight is $700{\text{ Wm}}^{-2}$ and it is absorbed by the water over an effective area of …

A current carrying wire heats a metal rod. The wire provides a constant power (P) to the rod. The metal rod is enclosed in an insulated container. It is observed that the temperature (T) in the metal rod changes with time (t) as : …

One mole of a monoatomic ideal gas goes through a thermodynamic cycle, as shown in the volume versus temperature (V-T) diagram. The correct statement(s) is/are :
[R is the gas constant]

A liquid at 30°C is poured very slowly into a Calorimeter that is at temperature of 110°C. The boiling temperature of the liquid is 80°C. It is found that the first 5 gm of the liquid completely evaporates. After pouring another 80 gm of the liquid the equilibrium temperature is …

A mixture of ideal gas containing 5 moles of monatomic gas and 1 mole of rigid diatomic gas is initially at pressure ${\mathrm{P}}_0$, volume ${\mathrm{V}}_0$ and temperature ${\mathrm{T}}_0$. If the gas mixture is adiabatically compressed to a volume ${\mathrm{V}}_0/4$ …

A small particle of mass m moving inside a heavy, hollow and straight tube along the tube axis undergoes elastic collision at two ends. The tube has no friction and it is closed at one end by a flat surface while the other end is fitted with a heavy movable flat piston as shown i …

In a thermodynamics process on an ideal monatomic gas, the infinitesimal heat absorbed by the gas is given by $\mathrm{T}\Delta \mathrm{X}$, where T is temperature of the system and $\Delta \mathrm{X}$ is the infinitesimal change in a thermodynamic quantity X of the system. …

In a thermodynamic process on an ideal monatomic gas, the infinitesimal heat absorbed by the gas is given by $\mathrm{T}\Delta \mathrm{X}$, where T is temperature of the system and $\Delta \mathrm{X}$ is the infinitesimal change in a thermodynamic quantity X of the system. F …

One mole of a monatomic ideal gas undergoes an adiabatic expansion in which its volume becomes eight times its initial value. If the initial temperature of the gas is $100K$ and the universal gas constant $R=8.0Jmo{l}^{-1}{K}^{-1}$, the decrease in its internal energy, in Jou …

One mole of a monatomic ideal gas undergoes four thermodynamic processes as shown schematically in the $PV$-diagram below. Among these four processes, one is isobaric, one is isochoric, one is isothermal and one is adiabatic. Match the processes mentioned in List-1 with the cor …

One mole of a monatomic ideal gas undergoes a cyclic process as shown in the figure (where $V$ is the volume and $T$ is the temperature). Which of the statements below is (are) true?

Two conducting cylinders of equal length but different radii are connected in series between two heat baths kept at temperatures $T_1=300K$ and $T_2=100K$, as shown in the figure. The radius of the bigger cylinder is twice that of the smaller one and the thermal conductivit …

A flat plate is moving normal to its plane through a gas under the action of a constant force $F$. The gas is kept at a very low pressure. The speed of the plate $v$ is much less than the average speed $u$ of the gas molecules. Which of the following options is/are true?

A human body has a surface area of approximately $1{\mathrm{m}}^2$. The normal body temperature is 10 K above the surrounding room temperature $T_0$. Take the room temperature to be $T_0=300\mathrm{K}$. For $T_0=300\mathrm{K}$, the value of …

An ideal gas is undergoing a cyclic thermodynamic process in different ways as shown in the corresponding $P-V$ diagrams in column 3 of the table. Consider only the path from state 1 to state 2. $W$ denotes the corresponding work done on the system. The equations and plots in …

An ideal gas is undergoing a cyclic thermodynamic process in different ways as shown in the corresponding $P-V$ diagrams in column 3 of the table. Consider only the path from state 1 to state 2. $W$ denotes the corresponding work done on the system. The equations and plots in …

An ideal gas is undergoing a cyclic thermodynamic process in different ways as shown in the corresponding $P-V$ diagrams in column 3 of the table. Consider only the path from state 1 to state 2. $W$ denotes the corresponding work done on the system. The equations and plots in …

A water cooler of storage capacity 120 litres can cool water at a constant rate of $P$ watts. In a closed circulation system (as shown schematically in the figure), the water from the cooler is used to cool an external device that generates constantly 3 kW of heat (thermal load …

An incandescent bulb has a thin filament of tungsten that is heated to high temperature by passing an electric current. The hot filament emits black-body radiation. The filament is observed to break up at random locations after a sufficiently long time of operation due to non-uni …

A metal is heated in a furnace where a sensor is kept above the metal surface to read the power radiated ($P$) by the metal. The sensor has a scale that displays ${\log }_2(P/P_0)$, where $P_0$ is a constant. When the metal surface is at a temperature of 487°C, the senso …

A gas is enclosed in a cylinder with a movable frictionless piston. Its initial thermodynamic state at pressure $P_i=10^5\mathrm{Pa}$ and volume $V_i=10^{-3}{\mathrm{m}}^3$ changes to a final state at $P_f=(1/32)\times 10^5\mathrm{Pa}$ and …

The ends Q and R of two thin wires, PQ and RS, are soldered (joined) together. Initially each of the wires has a length of 1 m at 10 °C. Now the end P is maintained at 10 °C, while the end S is heated and maintained at 400 °C. The system is thermally insulated from its surroundin …

Two spherical stars $A$ and $B$ emit blackbody radiation. The radius of $A$ is 400 times that of $B$ and $A$ emits $10^4$ times the power emitted from $B$. The ratio $\left(\frac{{\lambda }_A}{{\lambda }_B}\right)$ of their wavelengths ${\lambda }_A$ and ${\lambda }_B$ at which the …

A container of fixed volume has a mixture of one mole of hydrogen and one mole of helium in equilibrium at temperature T. Assuming the gases are ideal, the correct statement(s) is (are)

An ideal monoatomic gas is confined in a horizontal cylinder by a spring loaded piston (as shown in the figure). Initially the gas is at temperature $T_1$, pressure $P_1$ and volume $V_1$ and the spring is in its relaxed state. The gas is then heated very slowly to temperature …

Parallel rays of light of intensity $I=912W{m}^{-2}$ are incident on a spherical black body kept in surroundings of temperature 300 K. Take Stefan-Boltzmann constant $\sigma =5.7\times 10^{-8}W{m}^{-2}{K}^{-4}$ and assume that the energy exchange with the surroundings is only thr …