Heat and Thermodynamics

If the temperature of a gas is increased from $127^{\circ} \mathrm{C}$ to $527^{\circ} \mathrm{C}$, then the rms speed of the gas molecules

If the radiation emitted by a perfect radiator has maximum intensity at a wavelength of $2900 \mathop {\rm{A}}\limits^{\rm{o}}$, the intensity of radiation emitted by it is
(Stefan-Boltzmann's constant $=5.67 \times 10^{-8} \mathrm{Wm}^{-2}...

The ratio of the work done, change in internal energy and heat absorbed when a diatomic gas expands at constant pressure is

When ' $n$ ' identical mercury drops combine to form a single big drop

The temperature of a body shown by a faulty Celsius thermometer is $49^{\circ} \mathrm{C}$ and by a correct Fahrenheit thermometer is $122^{\circ} \mathrm{F}$. The correction to be applied to the faulty thermometer is

A metal metre scale that is accurate up to 0.5 mm is made at a temperature of $25^{\circ} \mathrm{C}$. The range of temperatures within which it can be used is (Coefficient of linear expansion of the metal $=10^{-5} /{ }^{\circ} \mathrm{C}$...

A Carnot engine uses diatomic gas as a working substance. During the adiabatic expansion part of the cycle, if the volume of the gas becomes 32 times its initial volume, then the efficiency of the engine is

The ratio of the average translational kinetic energies of hydrogen and oxygen at the same temperature is

A steel pendulum clock manufactured at $32^{\circ} \mathrm{C}$ and working at $47^{\circ} \mathrm{C}$ is nearly
(Coefficient of linear expansion of steel $=12 \times 10^{-6} /{ }^{\circ} \mathrm{C}$ )

Three moles of an ideal gas undergoes a cyclic process $A B C A$ as shown in the figure. The pressure, volume and absolute temperature at points $A, B$ and $C$ are respectively $\left(p_1, V_1, T_1\right),\left(p_2, 3 V_1, T_1\right)$ and $...

The pressure of a mixture of 64 g of oxygen, 28 g of nitrogen and 132 g of carbon dioxide gases in a closed vessel is $p$. Under isothermal conditions if entire oxygen is removed from the vessel, the pressure of the mixture of remaining two...

The power of a refrigerator that can make 15 kg of ice at $0^{\circ} \mathrm{C}$ from water at $30^{\circ} \mathrm{C}$ in one hour is

To increase the length of a metal rod by $0.4 \%$ the temperature of the rod is to be increased by (Coefficient of linear expansion of the metal $\left.=20 \times 10^{-6}{ }^{\circ} \mathrm{C}^{-1}\right)$

At constant pressure, equal amounts of heat are supplied to a monoatomic gas and a diatomic gas separately. The ratio of the increases in internal energies of the two gases is

A rectangular ice box of total surface area of $1000 \mathrm{~cm}^2$ initially contains 1.5 kg of ice at $0^{\circ} \mathrm{C}$. If the thickness of the walls of the box is 2 mm and the temperature outside the box is $42^{\circ} \mathrm{C}$...

If the rms speed of the molecules of a gas at a temperature of $77^{\circ} \mathrm{C}$ is $50 \mathrm{~ms}^{-1}$, then the rms speed of the same gas molecules at a temperature of $150.5^{\circ} \mathrm{C}$ is

The temperature at which the reading on Fahrenheit scale becomes $90 \%$ more than the reading on Celsius scale is

The molar specific heat of a monoatomic gas at constant pressure is
(Universal gas constant $=8.3 \mathrm{~J} \mathrm{~mol}^{-1} \mathrm{~K}^{-1}$ )

Two moles of a gas at a temperature of $327^{\circ} \mathrm{C}$ expands adiabatically such that its volume increases by $700 \%$. If the ratio of the specific heat capacities of the gas is $\frac{4}{3}$, then the work done by the gas is (Un...

The heat required to convert 8 g of ice at a temperature of $-20^{\circ} \mathrm{C}$ to steam at $100^{\circ} \mathrm{C}$ is [specific heat capacity of ice $=2100 \mathrm{Jkg}^{-1} \mathrm{~K}^{-1}$, specific heat capacity of water $=4200 \...

The length of a metal rod is 20 cm and its area of cross-section is $4 \mathrm{~cm}^2$. If one end of the rod is kept at a temperature of $100^{\circ} \mathrm{C}$ and the other end is kept in ice at $0^{\circ} \mathrm{C}$, then the mass of ...

A gas is suddenly compressed such that its absolute temperature is doubled. If the ratio of the specific heat capacities of the gas is 1.5 , then the percentage decrease in the volume of the gas is

When the temperature of a gas in a closed vessel is increased by $2.4^{\circ} \mathrm{C}$, its pressure increases by $0.5 \%$. The initial temperature of the gas is

If the heat required to increase the rms speed of 4 moles of a diatomic gas from $v$ to $\sqrt{3} v$ is 83.1 kJ , then the initial temperature of the gas is
(universal gas constant $=8.31 \mathrm{~J} \mathrm{~mol}^{-1} \mathrm{~K}^{-1}$ )

A body cools from a temperature of $60^{\circ} \mathrm{C}$ to $50^{\circ} \mathrm{C}$ in 10 minutes and $50^{\circ} \mathrm{C}$ to $40^{\circ} \mathrm{C}$ in 15 minutes. The time taken in minutes for the body to cool from $40^{\circ} \mathr...

The efficiency of a reversible heat engine working between two temperatures is $50 \%$. The coefficient of performance of a refrigerator working between the same two temperatures but in reverse direction is

The temperature on a fahrenheit temperature scale that is twice the temperature on a celsius temperature scale is

The temperatures of equal masses of three different liquids $A, B$ and $C$ are $15^{\circ} \mathrm{C}, 24^{\circ} \mathrm{C}$ and $30^{\circ} \mathrm{C}$, respectively. The resultant temperature when liquids $A$ and $B$ are mixed is $20^{\c...

The total internal energy of 4 moles of a diatomic gas at a temperature of $27^{\circ} \mathrm{C}$ is (gas constant $=831$ $\mathrm{J} \mathrm{mol}^{-1} \mathrm{~K}^{-1}$ )

If $d Q, d U$ and $d W$ are heat energy absorbed, change in internal energy and external work done respectively by a diatomic gas at constant pressure, then $d W: d U: d Q$ is

A solid sphere at a temperature $T \mathrm{~K}$ is cut in to two hemisphere. The ratio of energies radiated by one hemisphere to the whole sphere per second is

When 54 g of ice at $-20^{\circ} \mathrm{C}$ is mixed with 25 g of steam at $100^{\circ} \mathrm{C}$, then the final mixture at thermal equilibrium contains

If the temperature of a gas increased from $27^{\circ} \mathrm{C}$ to $159^{\circ} \mathrm{C}$, the increase in the rms speed of the gas molecules is

For a gas in a thermodynamic process, the relation between internal energy $U$, the pressure $p$ and the volume $V$ is $U=3+15 p V$. The ratio of the specific heat capacities of the gas at constant volume and constant pressure is

A pendulum clock loses 10.8 s a day when the temperature is $38^{\circ} \mathrm{C}$ and gains 108 s a day when the temperature is $18^{\circ} \mathrm{C}$. The coefficient of linear expansion of the metal of the pendulum clock is

A liquid cools from a temperature of 368 K to 358 K in 22 min . In the same room, the same liquid takes 12.5 min to cool from 358 K to 353 K . The room temperature is

At a pressure $p$ and temperature $127^{\circ} \mathrm{C}$, a vessel contains 21 g of a gas. A small hole is made into the vessel, so that the gas in it leaks out. At a pressure of $\frac{2 p}{3}$ and a temperature of $t^{\circ} \mathrm{C}$...

The ratio of the specific heat capacities of a gas is 1.5 . When the gas undergoes adiabatic process, its volume is doubled and pressure becomes $p_1$. When the gas undergoes isothermal process, its volume is doubled and pressure becomes $p...

A big liquid drop splits into $n$ similar small drops under isothermal conditions, then in the process

A vessel contains hydrogen and nitrogen gases in the ratio $2: 3$ by mass. If the temperature of the mixture of the gases is $30^{\circ} \mathrm{C}$, then the ratio of the average kinetic energies per molecule of hydrogen and nitrogen gases...

The thickness of a uniform rectangular metal plate is 5 mm and the area of each surface is $5 \mathrm{~cm}^5$. In steady state, the temperature difference between the two surfaces of the plate is $14^{\circ} \mathrm{C}$. If the heat flowing...

37 g of ice at $0^{\circ} \mathrm{C}$ temperature is mixed with 74 g of water at $70^{\circ} \mathrm{C}$ temperature. The resultant temperature is (specific heat capacity of water $=1 \mathrm{cal} {\mathrm{g}^{-1o}} \mathrm{C}^{-1}$ and lat...

The temperature difference between the ends of two cylindrical rods $A$ and $B$ of the same material is $2: 3$. In steady state the ratio of the rates of flow of heat through the rods $A$ and $B$ is $5: 9$. If the radii of the rods $A$ and ...

The temperature at which the rms speed of oxygen molecules is $75 \%$ or rms speed of nitrogen molecules at a temperature of $287^{\circ} \mathrm{C}$

When $Q_{1}$ amount of heat supplied to a monoatomic gas, the work done by the gas is $W$. When $Q_{2}$ amount of heat is supplied to a diatomic gas, the work done by the gas is $2 W$. Then, $Q_{1}: Q_{2}$.

Steam of mass 60 g at a temperature $100^{\circ} \mathrm{C}$ is mixed with water of mass 360 g at a temperature $40^{\circ} \mathrm{C}$. The ratio of the masses of steam and water in equilibrium is (Latent heat of steam is $540 \mathrm{cal}...

The Fahrenheit and Kelvin scales of temperature will have the same reading at a temperature of

If the ratio of densities of two substances is $5: 6$ and the ratio of their specific heat capacities is $3: 5$, then the ratio of heat energies required per unit volume so that the two substances can have same temperature rise is

In a process, the work done by the system is equal to the decrease in its internal energy. The process that the system undergoes is

N molecules each of mass $m$ of gas $A$ and 2 N molecules each of mass 2 m of gas $B$ are contained in a vessel which is maintained at a temperature $T$. The mean square velocity of the molecules of gas $B$ is denoted by $v_2^2$ and the mea...