Heat & Thermodynamics — JEE Main PYQs

A sample of an ideal gas is taken through the cyclic process ABCA as shown in figure. It absorbs, 40 J of heat during the part AB, no heat during BC and rejects 60 J of heat during CA. A work 50 J is done on the gas during the part BC. The internal energy of the gas at A is 1560 …

What will be the effect on the root mean square velocity of oxygen molecules if the temperature is doubled and oxygen molecule dissociates into atomic oxygen?

For a perfect gas, two pressures ${\mathrm{P}}_1$ and ${\mathrm{P}}_2$ are shown in figure. The graph shows:

According to kinetic theory of gases,
A. The motion of the gas molecules freezes at $0^{\circ }\mathrm{C}$
B. The mean free path of gas molecules decreases if the density of molecules is increased.
C. The mean free path of gas molecules increases if temperature is increased kee …

A lead bullet penetrates into a solid object and melts. Assuming that $40\%$ of its kinetic energy is used to heat it, the initial speed of bullet is:
(Given, initial temperature of the bullet $=127^{\circ }\mathrm{C}$, Melting point of the bullet $=327^{\circ }\mathrm{C}$ …

A diatomic gas $(\gamma =1.4)$ does 400 J of work when it is expanded isobarically. The heat given to the gas in the process is ______ J.

The total internal energy of two mole monoatomic ideal gas at temperature $\mathrm{T}=300\mathrm{K}$ will be ____ J. (Given $\mathrm{R}=8.31\mathrm{J}/\mathrm{mol}\cdot \mathrm{K}$)

At what temperature a gold ring of diameter 6.230 cm be heated so that it can be fitted on a wooden bangle of diameter 6.241 cm ? Both the diameters have been measured at room temperature ($27^{\circ }\mathrm{C}$).
(Given: coefficient of linear thermal expansion of gold …

Starting with the same initial conditions, an ideal gas expands from volume ${\mathrm{V}}_1$ to ${\mathrm{V}}_2$ in three different ways. The work done by the gas is ${\mathrm{W}}_1$ if the process is purely isothermal, ${\mathrm{W}}_2$ if the process is purely adiabatic and …

A vessel contains 16 g of hydrogen and 128 g of oxygen at standard temperature and pressure. The volume of the vessel in ${\mathrm{cm}}^3$ is :

A flask contains argon and oxygen in the ratio of 3:2 in mass and the mixture is kept at $27^{\circ }\mathrm{C}$. The ratio of their average kinetic energy per molecule respectively will be :

A geyser heats water flowing at a rate of 2.0 kg per minute from $30^{\circ }\mathrm{C}$ to $70^{\circ }\mathrm{C}$. If geyser operates on a gas burner, the rate of combustion of fuel will be _____ $\mathrm{g}{\min }^{-1}$
[Heat of combustion …

A heat engine operates with the cold reservoir at temperature 324 K.

The minimum temperature of the hot reservoir, if the heat engine takes 300 J heat from the hot reservoir and delivers 180 J heat to the cold reservoir per cycle, is ______ K.

A cylinder of fixed capacity of 44.8 litres contains helium gas at standard temperature and pressure. The amount of heat needed to raise the temperature of gas in the cylinder by $20.0^{\circ }\mathrm{C}$ will be:
(Given gas constant $R=8.3{\mathrm{JK}}^{-1}{\mathrm{mol}}^{-1}$)

As per the given figure, two plates A and B of thermal conductivity K and 2 K are joined together to form a compound plate. The thickness of plates are 4.0 cm and 2.5 cm respectively and the area of cross-section is $120{\mathrm{cm}}^2$ for each plate. The equivalent thermal co …

300 cal. of heat is given to a heat engine and it rejects 225 cal. of heat. If source temperature is $227^{\circ }\mathrm{C}$, then the temperature of sink will be ____ ${}^{\circ }\mathrm{C}$.

The efficiency of a Carnot's engine, working between steam point and ice point, will be :

A thermally insulated vessel contains an ideal gas of molecular mass M and ratio of specific heats 1.4. Vessel is moving with speed v and is suddenly brought to rest. Assuming no heat is lost to the surrounding and vessel temperature of the gas increases by : ($\mathrm{R}=$ uni …

A mixture of hydrogen and oxygen has volume $2000{\mathrm{cm}}^3$, temperature 300 K , pressure 100 kPa and mass 0.76 g The ratio of number of moles of hydrogen to number of moles of oxygen in the mixture will be :

In a carnot engine, the temperature of reservoir is $527^{\circ }\mathrm{C}$ and that of sink is 200 K . If the workdone by the engine when it transfers heat from reservoir to sink is 12000 kJ , the quantity of heat absorbed by the engine from reservoir is ____ …

The pressure $P_1$ and density $d_1$ of diatomic gas $\left(\gamma =\frac{7}{5}\right)$ changes suddenly to ${\mathrm{P}}_2\left(>{\mathrm{P}}_1\right)$ and ${\mathrm{d}}_2$ respectively during an adiabatic process. The temperature of the gas increases and becomes
_ …

One mole of a monoatomic gas is mixed with three moles of a diatomic gas. The molecular specific heat of mixture at constant volume is $\frac{{\alpha }^2}{4}\mathrm{RJ}/\mathrm{mol}\mathrm{K}$; then the value of $\alpha$ will be ____ . (Assume that the given …

A Carnot engine whose heat sinks at $27^{\circ }\mathrm{C}$, has an efficiency of $25\%$. By how many degrees should the temperature of the source be changed to increase the efficiency by $100\%$ of the original efficiency ?

Two metallic blocks ${\mathrm{M}}_1$ and ${\mathrm{M}}_2$ of same area of cross-section are connected to each other (as shown in figure). If the thermal conductivity of ${\mathrm{M}}_2$ is K then the thermal conductivity of ${\mathrm{M}}_1$ will be : [Assume steady state heat con …

0.056 kg of Nitrogen is enclosed in a vessel at a temperature of $127^{\circ }\mathrm{C}$. The amount of heat required to double the speed of its molecules is ______ k cal. (Take $\mathrm{R}=2$ cal mole${}^{-1}{\mathrm{K}}^{-1}$ )

A Carnot engine takes 5000 kcal of heat from a reservoir at $727^{\circ }$C and gives heat to a sink at $127^{\circ }$C. The work done by the engine is :

A 100 g of iron nail is hit by a 1.5 kg hammer striking at a velocity of $60{\mathrm{ms}}^{-1}$. What will be the rise in the temperature of the nail if one fourth of energy of the hammer goes into heating the nail?
[Specific heat capacity of iron …

A monoatomic gas performs a work of $\frac{\mathrm{Q}}{4}$ where Q is the heat supplied to it. The molar heat capaticy of the gas will be $\_\_\_\_$ R during this transformation.

Where $R$ is the gas constant.

In an experment ot verify Newton's law of cooling, a graph is plotted between, the temperature difference $(\Delta T)$ of the water and surroundings and time as shown in figure. The initial temperature of water is taken as $80^{\circ }C$. The value of $t_2$ as mentioned in the …

A solid metallic cube having total surface area 24 ${\mathrm{m}}^2$ is uniformly heated. If its temperature is increased by $10^{\circ }\mathrm{C}$, calculate the increase in volume of the cube (Given : $\alpha =5.0\times 10^{-4}{}^{\circ }{\mathrm{C}}^{-1}$ )

A copper block of mass 5.0 kg is heated to a temperature of $500^{\circ }\mathrm{C}$ and is placed on a large ice block. What is the maximum amount of ice that can melt? [Specific heat of copper: $0.39{\mathrm{Jg}}^{-1}{}^{\circ }{\mathrm{C}}^{-1}$ and latent heat of fusion of …

The ratio of specific heats $\left(\frac{{\mathrm{C}}_{\mathrm{P}}}{{\mathrm{C}}_{\mathrm{V}}}\right)$ in terms of degree of freedom (f) is given by:

When a gas filled in a closed vessel is heated by raising the temperature by $1^{\circ }\mathrm{C}$, its pressure increase by $0.4\%$. The initial temperature of the gas is $\_\_\_\_$ K.

The relation between root mean square speed $\left({\mathrm{v}}_{\mathrm{rms}}\right)$ and most probable speed ( ${\mathrm{v}}_{\mathrm{p}}$ ) for the molar mass M of oxygen gas molecule at the temperature of 300 K will be :-

A steam engine intakes 50 g of steam at $100^{\circ }\mathrm{C}$ per minute and cools it down to $20^{\circ }\mathrm{C}$. If latent heat of vaporization of steam is $540{\mathrm{cal}\mathrm{g}}^{-1}$, then the heat rejected by the steam engine per minute is ______ …

The rms speed of the molecules of Hydrogen, Oxygen and Carbondioxide at the same temperature are ${\mathrm{V}}_{\mathrm{H}}$, ${\mathrm{V}}_{\mathrm{O}}$ and ${\mathrm{V}}_{\mathrm{C}}$ respectively then:

An electric appliance supplies $6000\mathrm{J}/\min$ heat to the system. If the system delivers a power of 90 W . How long it would take to increase the internal energy by $2.5\times 10^3\mathrm{J}$ ?

Each side of a box made of metal sheet in cubic shape is '$a$' at room temperature '$T$', the coefficient of linear expansion of the metal sheet is '$\alpha$'. The metal sheet is heated uniformly, by a small temperature $\Delta \mathrm{T}$, so that its new temperature is …

Match List I with List II.

List I
(a) Isothermal
(b) Isochoric
(c) Adiabatic
(d) Isobaric

List II
(i) Pressure constant
(ii) Temperature constant
(iii) Volume constant
(iv) Heat content is constant

Choose the correct answer from the options given below:

$n$ mole of perfect gas undergoes a cyclic process ABCA (see figure) consisting of the following processes.
$A\to B$ : Isothermal expansion at temperature T so that the volume is doubled from $V_1$ to $V_2=2V_1$ and Pressure changes from $P_1$ to $P_2$. …

A refrigerator consumes an average 35 W power to operate between temperature $-10^{\circ }\mathrm{C}$ to $25^{\circ }\mathrm{C}$. If there is no loss of energy then how much average heat per second does it transfer?

A cylindrical container of volume $4.0\times 10^{-3}{\mathrm{m}}^3$ contains one mole of hydrogen and two moles of carbon dioxide. Assume the temperature of the mixture is 400 K . The pressure of the mixture of gases is: [Take gas constant as …

The temperature of equal masses of three different liquids $x,y$ and $z$ are $10^{\circ }\mathrm{C},20^{\circ }\mathrm{C}$ and $30^{\circ }\mathrm{C}$ respectively. The temperature of mixture when x is mixed with y is $16^{\circ }\mathrm{C}$ and that when y is mixed with z is …

The amount of heat needed to raise the temperature of 4 moles of a rigid diatomic gas from $0^{\circ }\mathrm{C}$ to $50^{\circ }\mathrm{C}$ when no work is done is ______. ($R$ is the universal gas constant)

Consider a mixture of gas molecule of types A, B and C having masses ${\mathrm{m}}_{\mathrm{A}}<{\mathrm{m}}_{\mathrm{B}}<{\mathrm{m}}_{\mathrm{C}}$. The ratio of their root mean square speeds at normal temperature and pressure is:

In the reported figure, heat energy absorbed by a system in going through a cyclic process is ____ $\pi \mathrm{J}$.

On the basis of kinetic theory of gases, the gas exerts pressure because its molecules:

If one mole of an ideal gas at ( $P_1{V}_1$ ) is allowed to expand reversibly and isothermally ( A to B ) its pressure is reduced to one- half of the original pressure (see figure). This is followed by a constant volume cooling till its pressure is reduced to one-fourth of the …

The root mean square speed of molecules of a given mass of a gas at $27^{\circ }\mathrm{C}$ and 1 atmosphere pressure is $200{\mathrm{ms}}^{-1}$. The root mean square speed of molecules of the gas at $127^{\circ }\mathrm{C}$ and 2 atmosphere pressure is …

The correct relation between the degrees of freedom $f$ and the ratio of specific heat $\gamma$ is :