Heat And Thermodynamics - Mechanics - Physics Previous Year Questions

Statement I Gas thermometers are less sensitive than liquid thermometers.

Statement II The ratio of universal gas constant and avogadro's number is called Boltzmann's constant.

Statement III The density of a given mass of a gas at constant pressure is inversely proportional to its absolute temperature.

The correct option among the following is

A hole of diameter 5 cm is drilled in a metal sheet at $30^{\circ} \mathrm{C}$. The linear expansion of metal is $2 \times 10^{-5} \mathrm{~K}^{-1}$. The diameter of the hole when the temperature is raised to $230^{\circ} \mathrm{C}$, is equal to

A metal cube absorbs 2100.0 J of heat when its temperature is raised by $2^{\circ} \mathrm{C}$. If the specific heat of the metal is $900 \mathrm{~J} \mathrm{~kg}^{-1} \mathrm{~K}^{-1}$, then the mass of the cube is

The net work done by an ideal gas going through the cycle as shown in the $p-V$ diagram below is

A diatomic gas $\left(C_p=\frac{7}{2} R\right)$ does 200 J of work when it is expanded isobarically. The heat given to the gas in the process is

An object cools from $100^{\circ} \mathrm{C}$ to $40^{\circ} \mathrm{C}$ in 10 min , when the surrounding temperature is $10^{\circ} \mathrm{C}$. Then the time taken by the object to cool from $70^{\circ} \mathrm{C}$ to $20^{\circ} \mathrm{C}$ is (take, $\ln 2=0.7, \ln 3=11, \ln 6=18$ )

1.00 kg of liquid water at $100^{\circ} \mathrm{C}$ undergoes a phase change into steam at $100^{\circ} \mathrm{C}$ at 1.0 atm (take it to be $1.00 \times 10^5 \mathrm{~Pa}$ ). The initial volume of the liquid water was $1.00 \times 10^{-3} \mathrm{~m}^3$ which is changed to $2.001 \mathrm{~m}^3$ of steam. Find the change in the internal energy of the system.

(Use heat of vaporisation $\simeq 2000 \mathrm{~kJ} / \mathrm{kg}$ )

A monoatomic gas does 100 J of work, when it is expanded isobarically. How much of heat is given to the gas in the process?

If the root mean square (rms) speed of nitrogen molecules at room temperature is $100 \mathrm{~m} / \mathrm{s}$, then the rms speed of helium molecule at the same temperature is

Find the ratio of the length of a steel rod and a copper rod, if the steel rod is 4 cm longer, then the copper rod at any temperature.

(The coefficient of linear expansion for steel and copper are $1.1 \times 10^{-5} /{ }^{\circ} \mathrm{C}$ and $1.7 \times 10^{-5} /{ }^{\circ} \mathrm{C}$, respectively)

Two rod of same area of cross-section have lengths $L$ and $2 L$ and coefficients of linear expansions $2 \alpha$ and $a$ respectively. If they are welded to form a composite rod of length $3 L$ then the coefficient of linear expansion of the composite rod is

An insulating cylinder contains 4 moles of an ideal diatomic gas. When a heat $Q$ is supplied to it, 2 moles of the gas molecules dissociate. If the temperature of the gas remains constant, then the value of $Q$ is ( $R=$ universal gas constant)

For a given mass of a gas at constant temperature, the volume and the pressure are $V$ and $p$ respectively. Then the slope of the graph drawn between $\log _e V$ on $X$-axis and $\log _e p$ on $Y$-axis is

An ideal gas at $127^{\circ} \mathrm{C}$ is compressed suddenly to $8 / 27 \mathrm{}$of its initial volume. If $\gamma=5 / 3$ for an ideal gas, then rise in its temperature is

The heat energy required to convert 10 kg of ice at $-10^{\circ} \mathrm{C}$ into water at $0^{\circ} \mathrm{C}$ is (specific heat capacity of ice $=0.5 \mathrm{calg}^{-1}$ and latent heat of fusion of ice $=80 \mathrm{calg}^{-1}$ )

When some amount of heat energy is supplied to a monatomic gas, the percentage of heat energy used for increasing the internal energy of the gas $(\gamma=5 / 3)$ is

The average energy possessed by an oscillator at a temperature 300 K is (Boltzmann constant $=1.38 \times 10^{-23} \mathrm{JK}^{-1}$ )

The length of a metal rod at $30^{\circ} \mathrm{C}$ is 30 cm . If its temperature is raised to $105^{\circ} \mathrm{C}$, its length is increased by 0.027 cm . Then, the coefficient of linear expansion of the metal is

If the reading in Fahrenheit scale is twice the reading in Celsius scale, then the reading in Fahrenheit scale is

Two identical containers $A$ and $B$ with frictionless pistons contain the same ideal gas at the same temperature and same volume $V$. The mass of the gas in $A$ is $m_A$ and that in $B$ is $m_B$. The gas in each cylinder is now allowed to expand isothermally to the same final volume $2 V$. The changes in the pressure of the gases in $A$ and $B$ are found to be $2 \Delta p$ and $3 \Delta p$ respectively. Then the relation between $m_A$ and $m_B$ is