Heat & Thermodynamics — JEE Main PYQs

Which one is the correct option for the two different thermodynamic processes?

What will be the average value energy along one degree of freedom for an ideal gas in thermal equilibrium at a temperature $T$ ? ( ${\mathrm{k}}_{\mathrm{B}}$ is Boltzmann constant)

Two moles of an ideal gas with $\frac{C_P}{C_V}=\frac{5}{3}$ are mixed with 3 moles of another ideal gas with $\frac{C_P}{C_V}=\frac{4}{3}$. The value of $\frac{C_P}{C_V}$ for the mixture is:

A litre of dry air at STP expands adiabatically to a volume of 3 litres. If $\gamma =1.40$, the work done by air is: ($3^{1.4}=4.6555$) [Take air to be an ideal gas]

A Carnot engine operates between two reservoirs of temperatures 900 K and 300 K . The engine performs 1200 J of work per cycle. The heat energy (in J) delivered by the engine to the low temperature reservoir, in a cycle is ____.

A non-isotropic solid metal cube has coefficients of linear expansion as: $5\times 10^{-5}/{}^{\circ }\mathrm{C}$ along the $\mathrm{x}=$ axis and $5\times 10^{-6}/{}^{\circ }\mathrm{C}$ along the y and the z -axis. If coefficient of volume expansion of the solid …

Two ideal Carnot engines operate in cascade (all heat given up by one engine is used by the other engine to produce work) between temperatures, $T_1$ and $T_2$. The temperature of the hot reservoir of the first engine is ${\mathrm{T}}_1$ and the temperature of the cold reserv …

Under an adiabatic process, the volume of an ideal gas gets doubled. Consequently the mean collision time between the gas molecule changes from ${\tau }_1$ to ${\tau }_2$. If $\frac{{\mathrm{C}}_{\mathrm{p}}}{{\mathrm{C}}_{\mathrm{v}}}=\gamma$ for the gas then a good estimate for …

M grams of steam at $100^{\circ }\mathrm{C}$ is mixed with 200 g of ice at its melting point in a thermally insulated container. If it produces liquid water at $40^{\circ }\mathrm{C}$ [heat of vaporization of water is $540\mathrm{cal}/\mathrm{g}$ and heat of fusion of ice is …

A thermodynamic cycle $xyzx$ is shown on a V-T diagram. The P-V diagram that best describes this cycle is: (diagrams are schematic and not to scale)

The plot that depicts the behavior of the mean free time $\tau$ (time between two successive collisions) for the molecules of an ideal gas, as a function of temperature (T), qualitatively, is: (Graphs are schematic and not drawn to scale)

A Carnot engine having an efficiency of $\frac{1}{10}$ is being used as a refrigerator. If the work done on the refrigerator is 10 J, the amount of heat absorbed from the reservoir at lower temperature is:

Consider a mixture of $n$ moles of helium gas and $2n$ moles of oxygen gas (molecules taken to be rigid) as an ideal gas. Its ${\mathrm{C}}_{\mathrm{P}}/{\mathrm{C}}_{\mathrm{V}}$ value will be

Three containers ${\mathrm{C}}_1$, ${\mathrm{C}}_2$ and ${\mathrm{C}}_3$ have water at different temperatures. The table below shows the final temperature T when different amounts of water (given in liters) are taken from each container and mixed (assume no loss of heat during th …

Starting at temperature 300 K, one mole of an ideal diatomic gas ($\gamma =1.4$) is first compressed adiabatically from volume $V_1$ to $V_2=\frac{V_1}{16}$. It is then allowed to expand isobarically to volume $2V_2$. If all the processes are the quasi-static then the fina …

Consider two ideal diatomic gases A and B at some temperature T . Molecules of the gas A are rigid, and have a mass m . Molecules of the gas B have an additional vibrational mode and have mass $\frac{m}{4}$. The ratio of the specific heats $(C_v^A$ and …

Which of the following is an equivalent cyclic process corresponding to the thermodynamic cyclic given in the figure? Where, $1\to 2$ is adiabatic. (Graphs are schematic and are not to scale)

Two different wires having lengths ${\mathrm{L}}_1$ and ${\mathrm{L}}_2$, and respective temperature coefficient of linear expansion ${\alpha }_1$ and ${\alpha }_2$, are joined end-to-end. Then the effective temperature coefficient of linear expansion is:

In adiabatic process, the density of a diatomic gas becomes 32 times its initial value. The final pressure of the gas is found to be $n$ times the initial pressure. The value of $n$ is:

Nitrogen gas is at $300^{\circ }$C temperature. The temperature (in K) at which the rms speed of a ${\mathrm{H}}_2$ molecule would be equal to the rms speed of a nitrogen molecule, is ____. (Molar mass of ${\mathrm{N}}_2$ gas 28 g).

Consider a gas of triatomic molecules. The molecules are assumed to be triangular and made of massless rigid rods whose vertices are occupied by atoms. The internal energy of a mole of the gas at temperature T is:

A balloon filled with helium ($32^{\circ }\mathrm{C}$ and 1.7 atm.) bursts. Immediately afterwards the expansion of helium can be considered as:

A bakelite beaker has volume capacity of 500 cc at $30^{\circ }\mathrm{C}$. When it is partially filled with ${\mathrm{V}}_{\mathrm{m}}$ volume (at $30^{\circ }\mathrm{C}$) of mercury, it is found that the unfilled volume of the beaker remains constant as temperature is varied. If …

A calorimeter of water equivalent 20 g contains 180 g of water at $25^{\circ }\mathrm{C}$, 'm' grams of steam at $100^{\circ }\mathrm{C}$ is mixed in it till the temperature of the mixture is $31^{\circ }\mathrm{C}$. The value of 'm' is close to (Latent heat of water …

A metallic sphere cools from $50^{\circ }\mathrm{C}$ to $40^{\circ }$ in 300 s . If atmospheric temperature around is $20^{\circ }\mathrm{C}$, then the sphere's temperature after the next 5 minutes will be close to:

To raise the temperature of a certain mass of gas by $50^{\circ }\mathrm{C}$ at a constant pressure, 160 calories of heat is required. When the same mass of gas is cooled by $100^{\circ }\mathrm{C}$ at constant volume, 240 calories of heat is released. How many degrees of freedom …

If minimum possible work is done by a refrigerator in converting 100 grams of water at $0^{\circ }\mathrm{C}$ to ice, how much heat (in calories) is released to the surroundings at temperature $27^{\circ }\mathrm{C}$ (Latent heat of ice $=80\mathrm{Cal}/$ gram) to the nearest in …

Three rods of identical cross-section and lengths are made of three different materials of thermal conductivity ${\mathrm{K}}_1$, ${\mathrm{K}}_2$ and ${\mathrm{K}}_3$, respectively. They are joined together at their ends to make a long rod (see figure). One end of the long rod i …

In a dilute gas at pressure P and temperature T, the mean time between successive collisions of a molecule varies with T as:

An engine operates by taking a monatomic ideal gas through the cycle shown in the figure. The percentage efficiency of the engine is close to ____.

A bullet of mass 5 g , traveling with a speed of $210\mathrm{m}/\mathrm{s}$, strikes a fixed wooden target. One half of its kinetic energy is converted into heat in the bullet while the other half is converted into heat in the wood. The rise of temperature of the bullet if th …

Number of molecules in a volume of $4{\mathrm{cm}}^3$ of a perfect monoatomic gas at some temperature T and at a pressure of 2 cm of mercury is close to? (Given, mean kinetic energy of a molecule (at T ) is …

Molecules of an ideal gas are known to have three translational degrees of freedom and two rotational degrees of freedom. The gas is maintained at a temperature of T.
The total internal energy, $U$ of a mole of this gas, and the value of …

Initially a gas of diatomic molecules is contained in a cylinder of volume ${\mathrm{V}}_1$ at a pressure $P_1$ and temperature 250 K . Assuming that $25\%$ of the molecules get dissociated causing a change in number of moles. The pressure of the resulting gas at tempera …

The specific heat of water $=4200\mathrm{J}{\mathrm{kg}}^{-1}{\mathrm{K}}^{-1}$ and the latent heat of ice $=3.4\times 10^5\mathrm{J}{\mathrm{kg}}^{-1}$. 100 grams of ice at $0^{\circ }\mathrm{C}$ is placed in 200 g of water at $25^{\circ }\mathrm{C}$. The amount of ice th …

Match the ${\mathrm{C}}_p/{\mathrm{C}}_{\mathrm{V}}$ ratio for ideal gases with different type of molecules:
| (B) Diatomic rigid molecule …

A closed vessel contains 0.1 mole of a monatomic ideal gas at 200 K. If 0.05 mole of the same gas at 400 K is added to it, the final equilibrium temperature (in K) of the gas in the vessel will be close to ____.

Match the thermodynamics processes taking place in a system with the correct conditions. In the table: $\Delta \mathrm{Q}$ is the heat supplied, $\Delta \mathrm{W}$ is the work done and $\Delta \mathrm{U}$ is change in internal energy of the system. Match the following:

Process: …

The change in the magnitude of the volume of an ideal gas when a small additional pressure $\Delta \mathrm{P}$ is applied at a constant temperature, is the same as the change when the temperature is reduced by a small quantity $\Delta \mathrm{T}$ at constant pressure. The initial …

Two identical beakers A and B contain equal volumes of two different liquids at $60^{\circ }\mathrm{C}$ each and left to cool down. Liquid in A has density of $8\times 10^2\mathrm{kg}/{\mathrm{m}}^3$ and specific heat of $2000{\mathrm{Jkg}}^{-1}{\mathrm{K}}^{-1}$ while liqu …

A thermally insulted vessel contains 150 g of water at $0^{\circ }\mathrm{C}$. Then the air from the vessel is pumped out a adiabatically. A fraction of water turns into ice and the rest evaporates at $0^{\circ }\mathrm{C}$ itself. The mass of evaporated water will be closes …

The temperature, at which the root mean square velocity of hydrogen molecules equals their escape velocity from the earth is closest to:
[Boltzmans Constant $k_B=1.38\times 10^{-23}$ J/K
Avogadro number $N_A=6.02\times 10^{26}$/kg
Radius of Earth: $6.4\times 10^6$ m
Gravitat …

The given diagram shows four processes i.e., isochoric, isobaric, isothermal and adiabatic. The correct assignment of the processes, in the same order is given by:

An HCl molecule has rotational, translational and vibrational motions. If the rms velocity of HCl molecules in its gaseous phase is $\bar{v}$, m is its mass and ${\mathrm{k}}_{\mathrm{B}}$ is Boltzmann constant, then its temperature will be:

Following figure shows two processes A and B for a gas. If $\Delta {\mathrm{Q}}_{\mathrm{A}}$ and $\Delta {\mathrm{Q}}_{\mathrm{B}}$ are the amount of heat absorbed by the system in two cases, and $\Delta {\mathrm{U}}_{\mathrm{A}}$ and $\Delta {\mathrm{U}}_{\mathrm{B}}$ are chang …

For a given gas at 1 atm pressure, rms speed of the molecules is $200\mathrm{m}/\mathrm{s}$ at $127^{\circ }\mathrm{C}$. At 2 atm pressure and at $227^{\circ }\mathrm{C}$, the rms speed of the molecules will be:

A heat source at $\mathrm{T}=10^3\mathrm{K}$ is connected to another heat reservoir at $\mathrm{T}=10^2\mathrm{K}$ by a copper slab which is 1 m thick. Given that the thermal conductivity of copper is $0.1{\mathrm{WK}}^{-1}{\mathrm{m}}^{-1}$, the energy flux through i …

Three Carnot engines operate in series between a heat source at a temperature ${\mathrm{T}}_1$ and a heat sink at temperature ${\mathrm{T}}_4$ (see figure). There are two other reservoirs at temperature $T_2$ and $T_3$, as shown, with $T_1>T_2>T_3>T_4$. The …

A thermometer graduated according to a linear scale reads a value ${\mathrm{x}}_0$ when in contact with boiling water, and $x_0/3$ when in contact with ice. What is the temperature of an object in ${}^0\mathrm{C}$, if this thermometer in the contact with the object reads …

A metal bal of mass 0.1 kg is heated upto $500^{\circ }\mathrm{C}$ and dropped into a vessel of heat capacity $800{\mathrm{JK}}^{-1}$ and containing 0.5 kg water. The initial temperature of water and vessel is $30^0\mathrm{C}$. What is the approximate percentage increment in th …