Heat & Thermodynamics · JEE Main previous year questions

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 :

1. A.300 K
2. B.1000 K
3. C.900 K
4. D.360 K

Match List I with List II $$\begin{array}{llll}& \text{List I}& & \text{List II}\\ \text{A.}& \text{Isothermal Process}& \text{I.}& \text{Work done by the gas decreases internal energy}\\ \text{B.}& \text{Adiabatic Process}& \text{II.}& \text{No change in internal energy}\\ \text{C.}& \text{Isochoric Process}& \text{III.}& \text{The heat absorbed goes partly to increase internal energy and partly to do work}\\ \text{D.}& \text{Isobaric Process}& \text{IV.}& \text{No work is done on or by the gas}\end{array}$$ Choose the correct answer from the options given below :

1. A.A-I, B-II, C-IV, D-III
2. B.A-II, B-I, C-III, D-IV
3. C.A-II, B-I, C-IV, D-III
4. D.A-I, B-II, C-III, D-IV

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 :-

1. A.$\frac{9}{2}R$
2. B.$\frac{5}{2}R$
3. C.$\frac{3}{2}R$
4. D.$\frac{7}{2}R$

$1\mathrm{g}$ 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 $1600\mathrm{c}{\mathrm{m}}^3$ during this phase change, then the increase in internal energy in the process will be :

1. A.$4800\mathrm{J}$
2. B.$4320\mathrm{J}$
3. C.$432000\mathrm{J}$
4. D.$4.32\times 10^8\mathrm{J}$

A hole is drilled in a metal sheet. At $27^{\circ }\mathrm{C}$, the diameter of hole is $5\mathrm{cm}$. When the sheet is heated to $177^{\circ }\mathrm{C}$, the change in the diameter of hole is $d\times 10^{-3}\mathrm{cm}$. The value of d will be ____ if coefficient of linear expansion of the metal is $1.6\times 10^{-5}{/}^{\circ }\mathrm{C}$.

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, $\frac{{\gamma }_1}{{\gamma }_2}$ is :

1. A.$\frac{35}{27}$
2. B.$\frac{25}{21}$
3. C.$\frac{21}{25}$
4. D.$\frac{27}{35}$

1. A.
2. B.
3. C.
4. D.

The pressure ${\mathrm{P}}_1$ and density ${\mathrm{d}}_1$ 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 ____ times of its initial temperature. (given $\frac{{\mathrm{d}}_2}{{\mathrm{d}}_1}=32$)

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 $\frac{{\alpha }^2}{4}\mathrm{R}J/mol\mathrm{K}$; then the value of $\alpha$ will be ____. (Assume that the given diatomic gas has no vibrational mode).

1. A.$-450\mathrm{J}$
2. B.$450\mathrm{J}$
3. C.$900\mathrm{J}$
4. D.$1350\mathrm{J}$

Nearly $10\%$ of the power of a $110\mathrm{W}$ light bulb is converted to visible radiation. The change in average intensities of visible radiation, at a distance of $1\mathrm{m}$ from the bulb to a distance of $5\mathrm{m}$ is $a\times 10^{-2}W/{\mathrm{m}}^2$. The value of 'a' will be ____.

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

1. A.$166.7\text{ K}$
2. B.$255.1\text{ K}$
3. C.$266.7\text{ K}$
4. D.$367.7\text{ K}$

Consider the efficiency of Carnot's engine is given by $\eta =\frac{\alpha \beta }{\sin \theta }{\log }_e\frac{\beta x}{kT}$, where $\alpha$ and $\beta$ are constants. If T is temperature, k is Boltzmann constant, $\theta$ is angular displacement and x has the dimensions of length. Then, choose the incorrect option :

1. A.Dimensions of $\beta$ is same as that of force.
2. B.Dimensions of ${\alpha }^{-1}x$ is same as that of energy.
3. C.Dimensions of ${\eta }^{-1}\sin \theta$ is same as that of $\alpha \beta$.
4. D.Dimensions of $\alpha$ is same as that of $\beta$.

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 $10^{\circ }\text{C}$ and $20^{\circ }\text{C}$. The thermal radiation emitted in a given time by P and Q are in the ratio $1:1.15$. C. A Carnot Engine working between $100\text{ K}$ and $400\text{ K}$ has an efficiency of $75\%$. D. When small temperature difference between a liquid and its surrounding is quadrupled, the rate of loss of heat of the liquid becomes twice. Choose the correct answer from the options given below :

1. A.A, B, C only
2. B.A, B only
3. C.A, C only
4. D.B, C, D only

1. A.same as the $1^{\mathrm{st}}$ case.
2. B.always greater than the $1^{\mathrm{st}}$ case.
3. C.always less than the $1^{\mathrm{st}}$ case.
4. D.may increase or decrease with respect to the $1^{\mathrm{st}}$ case.

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

1. A.0.41
2. B.0.56
3. C.0.73
4. D.0.70

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

A sample of monoatomic gas is taken at initial pressure of $75\text{ kPa}$. The volume of the gas is then compressed from $1200{\text{ cm}}^3$ to $150{\text{ cm}}^3$ adiabatically. In this process, the value of workdone on the gas will be :

1. A.$79\text{ J}$
2. B.$405\text{ J}$
3. C.$4050\text{ J}$
4. D.$9590\text{ J}$

1. A.$20\mathrm{J}$
2. B.$30\mathrm{J}$
3. C.$-30\mathrm{J}$
4. D.$-60\mathrm{J}$

In a carnot engine, the temperature of reservoir is $527^{\circ }\mathrm{C}$ and that of sink is $200\mathrm{K}$. If the work done by the engine when it transfers heat from reservoir to sink is $12000\mathrm{kJ}$, the quantity of heat absorbed by the engine from reservoir is ____ $\times 10^6\mathrm{J}$.

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

1. A.$125{\text{ ms}}^{-1}$
2. B.$500{\text{ ms}}^{-1}$
3. C.$250{\text{ ms}}^{-1}$
4. D.$600{\text{ ms}}^{-1}$

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

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)

1. A.$\frac{M{v}^2}{7R}$
2. B.$\frac{M{v}^2}{5R}$
3. C.$2\frac{M{v}^2}{7R}$
4. D.$7\frac{M{v}^2}{5R}$

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

1. A.26.81%
2. B.37.81%
3. C.47.81%
4. D.57.81%

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