Heat & Thermodynamics — JEE Main PYQs

A sample of gas at temperature $T$ is adiabatically expanded to double its volume. The work done by the gas in the process is (given, $\gamma =\frac{3}{2}$):

The average kinetic energy of a molecule of the gas is

1 g of a liquid is converted to vapour at $3\times 10^5\mathrm{Pa}$ pressure. If $10\%$ of the heat supplied is used for increasing the volume by $1600{\mathrm{cm}}^3$ during this phase change, then the increase in internal energy in the process will be :

Given below are two statements :

Statements I : The temperature of a gas is $-73^{\circ }\mathrm{C}$. When the gas is heated to $527^{\circ }\mathrm{C}$, the root mean square speed of the molecules is doubled.
Statement II : The product of pressure and volume of an ideal gas …

A hole is drilled in a metal sheet. At $27^{\circ }\mathrm{C}$, the diameter of hole is 5 cm . When the sheet is heated to $177^{\circ }\mathrm{C}$, the change in the diameter of hole is $\mathrm{d}\times 10^{-3}\mathrm{cm}$. The value of d will be ____ if coefficien …

Let ${\gamma }_1$ be the ratio of molar specific heat at constant pressure and molar specific heat at constant volume of a monoatomic gas and ${\gamma }_2$ be the similar ratio of diatomic gas. Considering the diatomic gas molecule as a rigid rotator, the ratio, …

In an Isothermal change, the change in pressure and volume of a gas can be represented for three different temperature; ${\mathrm{T}}_3>{\mathrm{T}}_2>{\mathrm{T}}_1$ as :

A Carnot engine with efficiency $50\%$ takes heat from a source at 600 K. In order to increase the efficiency to $70\%$, keeping the temperature of sink same, the new temperature of the source will be:

The root mean square velocity of molecules of gas is

A bowl filled with very hot soup cools from $98^{\circ }\mathrm{C}$ to $86^{\circ }\mathrm{C}$ in 2 minutes when the room temperature is $22^{\circ }\mathrm{C}$. How long it will take to cool from $75^{\circ }\mathrm{C}$ to $69^{\circ }\mathrm{C}$ ?

According to law of equipartition of energy the molar specific heat of a diatomic gas at constant volume where the molecule has one additional vibrational mode is :-

The graph between two temperature scales P and Q is shown in the figure. Between upper fixed point and lower fixed point there are 150 equal divisions of scale P and 100 divisions on scale Q . The relationship for conversion between the two scales is given by :

Match List I with List II :

List I:
A. Isothermal Process
B. Adiabatic Process
C. Isochoric Process
D. Isobaric Process

List II:
I. Work done by the gas decreases internal energy
II. No change in internal energy
III. The heat absorbed goes partly to increase internal energy and …

Given below are two statements. One is labelled as Assertion A and the other is labelled as Reason R.
Assertion A : If dQ and dW represent the heat supplied to the system and the work done on the system respectively. Then according to the first law of thermodynamics …

A bicycle tyre is filled with air having pressure of 270 kPa at $27^{\circ }\mathrm{C}$. The approximate pressure of the air in the tyre when the temperature increases to $36^{\circ }\mathrm{C}$ is

A body cools from $60^{\circ }\mathrm{C}$ to $40^{\circ }\mathrm{C}$ in 6 minutes. If, temperature of surroundings is $10^{\circ }\mathrm{C}$. Then, after the next 6 minutes, its temperature will be ______ ${}^{\circ }\mathrm{C}$.

At 300 K, the rms speed of oxygen molecules is $\sqrt{\frac{\alpha +5}{\alpha }}$ times to that of its average speed in the gas. Then, the value of $\alpha$ will be (used $\pi =\frac{22}{7}$)

Heat energy of 184 kJ is given to ice of mass 600 g at $-12^{\circ }C$. Specific heat of ice is $2222.3{\text{J kg}}^{-1\circ }{\text{C}}^{-1}$ and latent heat of ice in $336{\text{kJ/kg}}^{-1}$
(A) Final temperature of system will be $0^{\circ }C$.
(B) Final temperature of the system w …

A flask contains hydrogen and oxygen in the ratio of $2:1$ by mass at temperature $27^{\circ }\mathrm{C}$. The ratio of average kinetic energy per molecule of hydrogen and oxygen respectively is :

Given below are two statements : one is labelled as Assertion A and the other is labelled as Reason R.
Assertion A : Efficiency of a reversible heat engine will be highest at $-273^{\circ }\mathrm{C}$ temperature of cold reservoir.
Reason R : The efficiency of Carnot's engine d …

A faulty thermometer reads $5^{\circ }\mathrm{C}$ in melting ice and $95^{\circ }\mathrm{C}$ in steam. The correct temperature on absolute scale will be ____ K when the faulty thermometer reads $41^{\circ }\mathrm{C}$.

The pressure $(\mathrm{P})$ and temperature $(\mathrm{T})$ relationship of an ideal gas obeys the equation ${\mathrm{PT}}^2=$ constant. The volume expansion coefficient of the gas will be:

Heat is given to an ideal gas in an isothermal process.
A. Internal energy of the gas will decrease.
B. Internal energy of the gas will increase.
C. Internal energy of the gas will not change.
D. The gas will do positive work.
E. The gas will do negative work.

Choose the correct …

The pressure of a gas changes linearly with volume from A to B as shown in figure. If no heat is supplied to or extracted from the gas then change in the internal energy of the gas will be

The correct relation between $\gamma =\frac{C_p}{C_v}$ and temperature T is :

Heat energy of 735 J is given to a diatomic gas allowing the gas to expand at constant pressure. Each gas molecule rotates around an internal axis but do not oscillate. The increase in the internal energy of the gas will be:

A hypothetical gas expands adiabatically such that its volume changes from 08 litres to 27 litres. If the ratio of final pressure of the gas to initial pressure of the gas is $\frac{16}{81}$. Then the ratio of $\frac{C_P}{C_V}$ will be.

A water heater of power 2000 W is used to heat water. The specific heat capacity of water is 4200 J ${\mathrm{kg}}^{-1}{\mathrm{K}}^{-1}$. The efficiency of heater is $70\%$. Time required to heat 2 kg of water from $10^{\circ }\mathrm{C}$ to $60^{\circ }\mathrm{C}$ is ______ s.
(Assu …

A Carnot engine operating between two reservoirs has efficiency $\frac{1}{3}$. When the temperature of cold reservoir raised by x, its efficiency decreases to $\frac{1}{6}$. The value of x, if the temperature of hot reservoir is $99^{\circ }\mathrm{C}$, will be:

For three low density gases A, B, C pressure versus temperature graphs are plotted while keeping them at constant volume, as shown in the figure.

The temperature corresponding to the point 'K' is:

A thermodynamic system is taken from an original state D to an intermediate state E by the linear process shown in the figure. Its volume is then reduced to the original volume from E to F by an isobaric process. The total work done by the gas from D to E to F will be

The root mean square speed of smoke particles of mass $5\times 10^{-17}\mathrm{kg}$ in their Brownian motion in air at NTP is approximately. [Given $\mathrm{k}=1.38\times 10^{-23}{\mathrm{JK}}^{-1}$]

A Carnot engine has efficiency of $50\%$. If the temperature of sink is reduced by $40^{\circ }\mathrm{C}$, its efficiency increases by $30\%$. The temperature of the source will be :

Given below are two statements :

Statement I : The average momentum of a molecule in a sample of an ideal gas depends on temperature.

Statement II : The rms speed of oxygen molecules in a gas is v. If the temperature is doubled and the oxygen molecules dissociate into oxygen at …

A vessel contains 14 g of nitrogen gas at a temperature of $27^{\circ }\mathrm{C}$. The amount of heat to be transferred to the gap to double the r.m.s. speed of its molecules will be : (Take $\mathrm{R}=8.32\mathrm{J}{\mathrm{mol}}^{-1}{\mathrm{k}}^{-1}$ )

At a certain temperature, the degrees of freedom per molecule for gas is 8. The gas performs 150 J of work when it expands under constant pressure. The amount of heat absorbed by the gas will be ______ J.

If ${\mathrm{K}}_1$ and ${\mathrm{K}}_2$ are the thermal conductivities, ${\mathrm{L}}_1$ and ${\mathrm{L}}_2$ are the lengths and ${\mathrm{A}}_1$ and ${\mathrm{A}}_2$ are the cross sectional areas of steel and copper rods respectively such that …

Read the following statements :
A. When small temperature difference between a liquid and its surrounding is doubled the rate of loss of heat of the liquid becomes twice.
B. Two bodies P and Q having equal surface areas are maintained at temperature $10^{\circ }\mathrm{C}$ and …

Same gas is filled in two vessels of the same volume at the same temperature. If the ratio of the number of molecules is $1:4$, then
A. The r.m.s. velocity of gas molecules in two vessels will be the same.
B. The ratio of pressure in these vessels will be $1:4$
C. The ratio …

A certain amount of gas of volume V at $27^{\circ }\mathrm{C}$ temperature and pressure $2\times 10^7{\mathrm{Nm}}^{-2}$ expands isothermally until its volume gets doubled. Later it expands adiabatically until its volume gets redoubled. The final pressure of the gas will be …

Following statements are given :
(1) The average kinetic energy of a gas molecule decreases when the temperature is reduced.
(2) The average kinetic energy of a gas molecule increases with increase in pressure at constant temperature.
(3) The average kinetic energy of a gas molec …

A unit scale is to be prepared whose length does not change with temperature and remains 20 cm, using a bimetallic strip made of brass and iron each of different length. The length of both components would change in such a way that difference between their lengths remains constan …

An ice cube of dimensions $60\mathrm{cm}\times 50\mathrm{cm}\times 20\mathrm{cm}$ is placed in an insulation box of wall thickness 1 cm. The box keeping the ice cube at $0^{\circ }\mathrm{C}$ of temperature is brought to a room of temperature $40^{\circ }\mathrm{C}$. The …

A gas has n degrees of freedom. The ratio of specific heat of gas at constant volume to the specific heat of gas at constant pressure will be :

In $1^{\text{st }}$ case, Carnot engine operates between temperatures 300 K and 100 K . In $2^{\text{nd }}$ case, as shown in the figure, a combination of two engines is used. The efficiency of this combination (in $2^{\text{nd }}$ case) will be :

Which statements are correct about degrees of freedom?
A. A molecule with $n$ degrees of freedom has $n^2$ different ways of storing energy.
B. Each degree of freedom is associated with $\frac{1}{2}\mathrm{RT}$ average energy per mole.
C. A monoatomic gas molecule has 1 …

Let ${\eta }_1$ is the efficiency of an engine at $T_1=447^{\circ }\mathrm{C}$ and $T_2=147^{\circ }\mathrm{C}$ while ${\eta }_2$ is the efficiency at $T_1=947^{\circ }\mathrm{C}$ and $T_2=47^{\circ }\mathrm{C}$. The ratio $\frac{{\eta }_1}{{\eta }_2}$ will be:

A block of ice of mass 120 g at temperature $0^{\circ }\mathrm{C}$ is put in 300 gm of water at $25^{\circ }\mathrm{C}$. The xg of ice melts as the temperature of the water reaches $0^{\circ }\mathrm{C}$. The value of x is
[Use: Specific heat capacity of water …

7 mole of certain monoatomic ideal gas undergoes a temperature increase of 40 K at constant pressure. The increase in the internal energy of the gas in this process is
(Given $\mathrm{R}=8.3{\mathrm{JK}}^{-1}{\mathrm{mol}}^{-1}$)

A monoatomic gas at pressure P and volume V is suddenly compressed to one eighth of its original volume. The final pressure at constant entropy will be: