JEE Main 2022 — Thermodynamics

The efficiency of a Carnot engine working between 127°C and 27°C is:

An ideal gas undergoes a cyclic process ABCA where AB is isothermal...

A $100g$ of iron nail is hit by a $1.5\mathrm{kg}$ 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 $=0.42{\mathrm{Jg}}^{-1}{C\circ }^{-1}$]

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 $1\mathrm{cm}$. The box keeping the ice cube at $0^{\circ}C$ of temperature is brought to a room of temperature $40^{\circ}C$. The rate of melting of ice is approximately: (Latent heat of fusion of ice is $3.4\times {10}^{5}J{\mathrm{kg}}^{-1}$ and thermal conducting of insulation wall is $0.05W{m}^{-1}^{\circ}{C}^{-1}$)

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 : ($R=$ universal gas constant)

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

A certain amount of gas of volume $V$ at $27^{\circ}C$ temperature and pressure $2\times {10}^{7}N{m}^{-2}$ expands isothermally until its volume gets doubled. Later it expands adiabatically until its volume gets redoubled. The final pressure of the gas will be (Use $\gamma =1.5$)

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

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 $\frac{1}{2}RT$ average energy per mole. C. A monoatomic gas molecule has $1$ rotational degree of freedom where as diatomic molecule has $2$ rotational degrees of freedom D. ${\mathrm{CH}}_{4}$ has a total to $6$ degrees of freedom. Choose the correct answer from the option given below:

Nearly $10%$ of the power of a $110W$ light bulb is converted to visible radiation. The change in average intensities of visible radiation, at a distance of $1m$ from the bulb to a distance of $5m$ is $a\times {10}^{-2}W{m}^{-2}$. The value of '$a$' 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 molecule decreases with increases in volume. (4) Pressure of a gas increases with increase in temperature at constant volume. (5) The volume of gas decreases with increase in temperature. Choose the correct answer from the options given below :

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

Starting with the same initial conditions, an ideal gas expands from volume ${V}_{1}$ to ${V}_{2}$ in three different ways. The work done by the gas is ${W}_{1}$ if the process is purely isothermal, ${W}_{2}$, if the process is purely adiabatic and ${W}_{3}$ if the process is purely isobaric. Then, choose the correct option

A geyser heats water flowing at a rate of $2.0\mathrm{kg}$ per minute from $30^{\circ}C$ to $70^{\circ}C$. If geyser operates on a gas burner, the rate of combustion of fuel will be _____ $g{\mathrm{min}}^{-1}$. [Heat of combustion $=8\times {10}^{3}{\mathrm{Jg}}^{-1}$, Specific heat of water $=4.2{\mathrm{Jg}}^{-1}{C\circ }^{-1}$]

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

If ${K}_{1}$ and ${K}_{2}$ are the thermal conductivities ${L}_{1}$ and ${L}_{2}$ are the lengths and ${A}_{1}$ and ${A}_{2}$ are the cross sectional areas of steel and copper rods respectively such that $\frac{{K}_{2}}{{K}_{1}}=9,\frac{{A}_{1}}{{A}_{2}}=2,\frac{{L}_{1}}{{L}_{2}}=2$. Then, for the arrangement as shown in the figure. The value of temperature $T$ of the steel - copper junction in the steady state will be 

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

As per the given figure, two plates $A$ and $B$ of thermal conductivity $K$ and $2K$ are joined together to form a compound plate. The thickness of plates are $4.0\mathrm{cm}$ and $2.5\mathrm{cm}$ respectively and the area of cross-section is $120{\mathrm{cm}}^{2}$ for each plate. The equivalent thermal conductivity of the compound plate is $(1+\frac{5}{\alpha })K$, then the value of $\alpha$ will be _____ . 

The total internal energy of two mole monoatomic ideal gas at temperature $T=300K$ will be _____ $J$. (Given $R=8.31J{\mathrm{mol}}^{-1}\cdot K$)

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

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

Two metallic wires of identical dimensions are connected is series. If ${\sigma }_{1}$ and ${\sigma }_{2}$ are the conductivities of the these wires respectively, the effective conductivity of the combination is :

A unit scale is to be prepared whose length does not change with temperature and remains $20\mathrm{cm}$, 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 constant. If length of brass is $40\mathrm{cm}$ and length of iron will be _____ $\mathrm{cm}$. $({\alpha }_{\mathrm{iron}}=1.2\times {10}^{-5}{K}^{-1}$ and ${\alpha }_{\mathrm{brass}}=1.8\times {10}^{-5}{K}^{-1})$.

A block of ice of mass $120g$ at temperature $0^{\circ}C$ is put in $300g$ of water at $25^{\circ}C$. The $xg$ of ice melts as the temperature of the water reaches $0^{\circ}C$. The value of $x$ is [Use: Specific heat capacity of water $=4200J{\mathrm{kg}}^{-1}{K}^{-1}$, Latent heat of ice $=3.5\times {10}^{5}J{\mathrm{kg}}^{-1}$]

At what temperature a gold ring of diameter $6.230\mathrm{cm}$ be heated so that it can be fitted on a wooden bangle of diameter $6.241\mathrm{cm}$? Both the diameters have been measured at room temperature $(27^{\circ}C)$. (Given: coefficient of linear thermal expansion of gold ${\alpha }_{L}=1.4\times {10}^{-5}{K}^{-1}$)

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 $=127^{\circ}C$, Melting point of the bullet $=327^{\circ}C$, Latent heat of fusion of lead $=2.5\times {10}^{4}J{\mathrm{kg}}^{-1}$, Specific heat capacity of lead $=125J\mathrm{kg}{K}^{-1}$)

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

Two metallic blocks ${M}_{1}$ and ${M}_{2}$ of same area of cross-section are connected to each other (as shown in figure). If the thermal conductivity of ${M}_{2}$ is $K$ then the thermal conductivity of ${M}_{1}$ will be : [Assume steady state heat conduction] 

A steam engine intakes $50g$ of steam at $100^{\circ}C$ per minute and cools it down to $20^{\circ}C$. If latent heat of vaporization of steam is $540\mathrm{cal}{g}^{-1}$, then the heat rejected by the steam engine per minute is _____ $\times {10}^{3}\mathrm{cal}$ (Given : specific heat capacity of water : $1\mathrm{cal}{g}^{-1}{C\circ }^{-1}$)

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 pressure ${P}_{1}$ and density ${d}_{1}$ of diatomic gas $(\gamma =\frac{7}{5})$ changes suddenly to ${P}_{2}(>{P}_{1})$ and ${d}_{2}$ respectively during an adiabatic process. The temperature of the gas increases and becomes____times of its initial temperature. (given $\frac{{d}_{2}}{{d}_{1}}=32$)

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

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

Statement - I : When $\mu$ amount of an ideal gas undergoes adiabatic change from state $({P}_{1},{V}_{1},{T}_{1})$ to state $({P}_{2},{V}_{2},{T}_{2})$, then work done is $W=\frac{\mu R({T}_{2}-{T}_{1})}{1-\gamma }$, where $\gamma =\frac{{C}_{P}}{{C}_{V}}$ and $R=$ universal gas constant. Statement - II : In the above case, when work is done on the gas, the temperature of the gas would rise.

For a perfect gas, two pressures ${P}_{1}$ and ${P}_{2}$ are shown in figure. The graph shows 

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 $20.0^{\circ}C$ will be (Given gas constant $R=8.3J{K}^{-1}{\mathrm{mol}}^{-1}$)

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 atoms, the rms speed will become $2v$. In the light of the above statements, choose the correct answer from the options given below :

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

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 $k=1.38\times {10}^{-23}J{K}^{-1}$]

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 $\frac{{\alpha }^{2}}{4}RJ\mathrm{mol}{K}^{-1}$; then the value of $\alpha$ will be _____ . (Assume that the given diatomic gas has no vibrational mode.)

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

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 of pressure will be $1:1$. $D$. The r.m.s. velocity of gas molecules in two vessels will be in the ratio of $1:4$.

A mixture of hydrogen and oxygen has volume $2000{\mathrm{cm}}^{3}$, temperature $300K$, pressure $100\mathrm{kPa}$ and mass $0.76g$. The ratio of number of moles of hydrogen to number of moles of oxygen in the mixture will be [Take gas constant $R=8.3J{K}^{-1}{\mathrm{mol}}^{-1}$]

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?

According to kinetic theory of gases, A. The motion of the gas molecules freezes at $0^{\circ}C$. 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 keeping pressure constant. D. Average kinetic energy per molecule per degree of freedom is $\frac{3}{2}{k}_{B}T$ (for monoatomic gases). Choose the most appropriate answer from the options given below

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

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

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

Resistance of the wire is measured as $2\Omega$ and $3\Omega$ at $10^{\circ}C$ and $30^{\circ}C$ respectively. Temperature coefficient of resistance of the material of the wire is

A copper block of mass $5.0\mathrm{kg}$ is heated to a temperature of $500^{\circ}C$ and is placed on a large ice block. What is the maximum amount of ice that can melt? [Specific heat of copper : $0.39{\mathrm{Jg}}^{-1}{C\circ }^{-1}$ and latent heat of fusion of water : $335{\mathrm{Jg}}^{-1}$]