Heat & Thermodynamics — JEE Main PYQs

A sample of 1 mole gas at temperature T is adiabatically expanded to double its volume. If adiabatic constant for the gas is $\gamma =\frac{3}{2}$, then the work done by the gas in the process is:

The temperature of a gas is $-78^{\circ }\mathrm{C}$ and the average translational kinetic energy of its molecules is K . The temperature at which the average translational kinetic energy of the molecules of the same gas becomes 2 K is :

A real gas within a closed chamber at $27^{\circ }\mathrm{C}$ undergoes the cyclic process as shown in figure. The gas obeys $P{V}^3=\mathrm{RT}$ equation for the path $A$ to $B$. The net work done in the complete cycle is (assuming $R=8\mathrm{J}/\mathrm{molK}$ ):

The total kinetic energy of 1 mole of oxygen at $27^{\circ }\mathrm{C}$ is:
[Use universal gas constant $(\mathrm{R})=8.31\mathrm{J}/$ mole K]

During an adiabatic process, the pressure of a gas is found to be proportional to the cube of its absolute temperature. The ratio of $\frac{{\mathrm{C}}_{\mathrm{p}}}{{\mathrm{C}}_{\mathrm{v}}}$ for the gas is :

The temperature of a gas having $2.0\times 10^{25}$ molecules per cubic meter at 1.38 atm (Given, $k=1.38\times 10^{-23}$ JK${}^{-1}$) is :

N moles of a polyatomic gas $(\mathrm{f}=6)$ must be mixed with two moles of a monoatomic gas so that the mixture behaves as a diatomic gas. The value of N is:

0.08 kg air is heated at constant volume through $5^{\circ }\mathrm{C}$. The specific heat of air at constant volume is $0.17\mathrm{kcal}/{\mathrm{kg}}^{\circ }\mathrm{C}$ and $\mathrm{J}=4.18$ joule $/\mathrm{cal}$. The change in its internal energy is approximately.

The average kinetic energy of a monatomic molecule is 0.414 eV at temperature :
(Use ${\mathrm{K}}_{\mathrm{B}}=1.38\times 10^{-23}\mathrm{J}/\mathrm{mol}-\mathrm{K}$)

A thermodynamic system is taken from an original state A to an intermediate state B by a linear process as shown in the figure. It's volume is then reduced to the original value from B to C by an isobaric process. The total work done by the gas from A to B and B to C would be :

Two vessels A and B are of the same size and are at same temperature. A contains 1 g of hydrogen and B contains 1g of oxygen. $P_A$ and $P_B$ are the pressures of the gases in A and B respectively, then $\frac{P_A}{P_B}$ is :

The parameter that remains the same for molecules of all gases at a given temperature is :

The given figure represents two isobaric processes for the same mass of an ideal gas, then

A diatomic gas $(\gamma =1.4)$ does 200 J of work when it is expanded isobarically. The heat given to the gas in the process is :

If the root mean square velocity of hydrogen molecule at a given temperature and pressure is $2\mathrm{km}/\mathrm{s}$, the root mean square velocity of oxygen at the same condition in $\mathrm{km}/\mathrm{s}$ is :

Two moles a monoatomic gas is mixed with six moles of a diatomic gas. The molar specific heat of the mixture at constant volume is:

The pressure and volume of an ideal gas are related as ${\mathrm{PV}}^{3/2}=\mathrm{K}$ (Constant). The work done when the gas is taken from state $\mathrm{A}\left({\mathrm{P}}_1,{\mathrm{V}}_1,{\mathrm{T}}_1\right)$ to state …

A block of ice at $-10^{\circ }\mathrm{C}$ is slowly heated and converted to steam at $100^{\circ }\mathrm{C}$. Which of the following curves represent the phenomenon qualitatively:

Choose the correct statement for processes A & B shown in figure.

If three moles of monoatomic gas $(\gamma =\frac{5}{3})$ is mixed with two moles of a diatomic gas $(\gamma =\frac{7}{5})$, the value of adiabatic exponent $\gamma$ for the mixture is:

Two thermodynamical process are shown in the figure. The molar heat capacity for process A and $B$ are $C_A$ and $C_B$. The molar heat capacity at constant pressure and constant volume are represented by ${\mathrm{C}}_{\mathrm{P}}$ and ${\mathrm{C}}_{\mathrm{V}}$, respe …

At which temperature the r.m.s. velocity of a hydrogen molecule equal to that of an oxygen molecule at $47^{\circ }\mathrm{C}$ ?

A gas mixture consists of 8 moles of argon and 6 moles of oxygen at temperature T. Neglecting all vibrational modes, the total internal energy of the system is

The temperature at which the kinetic energy of oxygen molecules becomes double than its value at $27^{\circ }\mathrm{C}$ is

Work done by a Carnot engine operating between temperatures $127^{\circ }\mathrm{C}$ and $27^{\circ }\mathrm{C}$ is 2 kJ. The amount of heat transferred to the engine by the reservoir is:

A steel rod of length 1 m and cross sectional area $10^{-4}{\mathrm{m}}^2$ is heated from $0^{\circ }\mathrm{C}$ to $200^{\circ }\mathrm{C}$ without being allowed to extend or bend. The compressive tension produced in the rod is $\_\_\_\_$ $\times 10^4\mathrm{N}$.
(Given Yo …

Given below are two statements:

Statement I: If heat is added to a system, its temperature must increase.

Statement II: If positive work is done by a system in a thermodynamic process, its volume must increase.

In the light of the above statements, choose the correct answer fr …

An air bubble of volume $1{\mathrm{cm}}^3$ rises from the bottom of a lake 40 m deep to the surface at a temperature of $12^{\circ }\mathrm{C}$. The atmospheric pressure is $1\times 10^5\mathrm{Pa}$, the density of water is $1000\mathrm{kg}/{\mathrm{m}}^3$ and …

The temperature of an ideal gas is increased from 200 K to 800 K. If r.m.s. speed of gas at 200 K is ${\mathrm{v}}_0$. Then, r.m.s. speed of the gas at 800 K will be:

A body cools in 7 minutes from $60^{\circ }\mathrm{C}$ to $40^{\circ }\mathrm{C}$. The temperature of the surrounding is $10^{\circ }\mathrm{C}$. The temperature of the body after the next 7 minutes will be:

A gas mixture consists of 2 moles of oxygen and 4 moles of neon at temperature T. Neglecting all vibrational modes, the total internal energy of the system will be :

A gas is compressed adiabatically, which one of the following statement is NOT true.

Consider two containers A and B containing monoatomic gases at the same Pressure (P), Volume (V) and Temperature (T). The gas in A is compressed isothermally to $\frac{1}{8}$ of its original volume while the gas B is compressed adiabatically to $\frac{1}{8}$ of its original v …

1 kg of water at $100^{\circ }\mathrm{C}$ is converted into steam at $100^{\circ }\mathrm{C}$ by boiling at atmospheric pressure. The volume of water changes from $1.00\times 10^{-3}{\mathrm{m}}^3$ as a liquid to $1.671{\mathrm{m}}^3$ as steam. The change in internal energy …

On a temperature scale ' X '. The boiling point of water is $65^{\circ }\mathrm{X}$ and the freezing point is $-15^{\circ }\mathrm{X}$. Assume that the X scale is linear. The equivalent temperature corresponding to $-95^{\circ }\mathrm{X}$ on the Farenheit scale would be:

Three vessels of equal volume contain gases at the same temperature and pressure. The first vessel contains neon (monoatomic). the second contains chlorine (diatomic) and third contains uranium hexafloride polyatomic). Arrange these on the basis of their root mean square speed ( …

If the r.m.s. speed of chlorine molecule is $490\text{ m/s}$ at $27^{\circ }C$, the r.m.s. speed of argon molecules at the same temperature will be (Atomic mass of argon $=39.9\text{ u}$, molecular mass of chlorine $=70.9\text{ u}$)

A body cools from $80^{\circ }\mathrm{C}$ to $60^{\circ }\mathrm{C}$ in 5 minutes. The temperature of the surrounding is $20^{\circ }\mathrm{C}$. The time it takes to cool from $60^{\circ }\mathrm{C}$ to $40^{\circ }\mathrm{C}$ is:

An engine operating between the boiling and freezing points of water will have

1. efficiency more than $27\%$
2. efficiency less than the efficiency a Carnot engine operating between the same two temperatures.
3. efficiency equal to $27\%$
4. efficiency less than $27\%$

The rms speed of oxygen molecule in a vessel at particular temperature is ${\left(1+\frac{5}{x}\right)}^{\frac{1}{2}}v$, where $v$ is the average speed of the molecule. The value of $x$ will be:(Take $\pi =\frac{22}{7}$ )

Under isothermal condition, the pressure of a gas is given by $P=a{V}^{-3}$, where a is a constant and V is the volume of the gas. The bulk modulus at constant temperature is equal to

The initial pressure and volume of an ideal gas are ${\mathrm{P}}_0$ and ${\mathrm{V}}_0$. The final pressure of the gas when the gas is suddenly compressed to volume $\frac{{\mathrm{V}}_0}{4}$ will be : (Given $\gamma =$ ratio of specific heats at constant pressure and at …

The mean free path of molecules of a certain gas at STP is 1500 d , where d is the diameter of the gas molecules. While maintaining the standard pressure, the mean free path of the molecules at 373 K is approximately :

Two plates A and B have thermal conductivities $84{\mathrm{Wm}}^{-1}{\mathrm{K}}^{-1}$ and $126{\mathrm{Wm}}^{-1}{\mathrm{K}}^{-1}$ respectively. They have same surface area and same thickness. They are placed in contact along their surfaces. If the temperatures of the outer surfaces …

A flask contains Hydrogen and Argon in the ratio 2:1 by mass. The temperature of the mixture is $30^{\circ }C$. The ratio of average kinetic energy per molecule of the two gases (K argon/K hydrogen) is: (Given: Atomic Weight of $Ar=39.9$)

A thermodynamic system is taken through cyclic process. The total work done in the process is :

The number of air molecules per ${\mathrm{cm}}^3$ increased from $3\times 10^{19}$ to $12\times 10^{19}$. The ratio of collision frequency of air molecules before and after the increase in number respectively is

A source supplies heat to a system at the rate of 1000 W. If the system performs work at a rate of 200 W. The rate at which internal energy of the system increases

The thermodynamic process, in which internal energy of the system remains constant is

The root mean square speed of molecules of nitrogen gas at $27^{\circ }\mathrm{C}$ is approximately:
(Given mass of a nitrogen molecule $=4.6\times 10^{-26}\mathrm{kg}$ and take Boltzmann constant ${\mathrm{k}}_{\mathrm{B}}=1.4\times 10^{-23}{\mathrm{JK}}^{-1}$ )