Heat and Thermodynamics

Equal volumes of two gases are kept in different containers having densities in the ratio 1 : 16. They exert equal pressures on the wall of their respective containers. Then the ratio of their r.m.s. velocities is

What is the ratio of the velocity of sound in hydrogen \(\left(\gamma=\frac{7}{5}\right)\) to that in helium \(\left(\gamma=\frac{5}{3}\right)\) at the same temperature? (Molecular weight of hydrogen and helium is 2 and 4 respectively.)

For a monoatomic gas, work done at constant pressure is W. The heat supplied at constant volume for the same rise in temperature of the gas is

Specific heats of an ideal gas at constant pressure and volume are denoted by \(\mathrm{C}_{\mathrm{p}}\) and \(\mathrm{C}_{\mathrm{v}}\) respectively. If \(\gamma=\frac{\mathrm{C}_{\mathrm{p}}}{\mathrm{C}_{\mathrm{v}}}\) and \(\mathrm{R}\)...

On an imaginary linear scale of temperature (called 'W' scale) the freezing and boiling points of water are 39\(^\circ\) W and 239\(^\circ\) W respectively. The temperature on the new scale corresponding to 39\(^\circ\)C temperature on Cels...

One mole of an ideal gas expands adiabatically at constant pressure such that its temperature \(T \propto {1 \over {\sqrt V }}\). The value of \(\gamma\) for the gas is (\(\gamma = {{{C_p}} \over {{C_v}}},V =\) Volume of the gas)

A perfectly black body emits a radiation at temperature 'T\(_1\)' K. If it is to radiate at 16 times this power, its temperature 'T\(_2\)' K should be

Two stars 'P' and 'Q' emit yellow and blue light respectively. The relation between their temperatures \(\left(\mathrm{T}_{\mathrm{P}}\right.\) and \(\left.\mathrm{T}_{\mathrm{Q}}\right)\) is

A conducting rod of length \(1 \mathrm{~m}\) has area of cross-section \(10^{-3} \mathrm{~m}^2\). One end is immersed in baiting water \(\left(100^{\circ} \mathrm{C}\right)\) and the other end in Ice \(\left(0^{\circ} \mathrm{C}\right)\). I...

A monoatomic gas is suddenly compressed to (1/8)th of its initial volume adiabatically. The ratio of the final pressure to initial pressure of the gas is (\(\gamma=5/3\))

A black rectangular surface of area '\(\mathrm{A}\)' emits energy '\(\mathrm{E}\)' per second at \(27^{\circ} \mathrm{C}\). If length and breadth is reduced to \((1 / 3)^{\text {rd }}\) of its initial value and temperature is raised to $$32...

The relation obeyed by a perfect gas during an adiabatic process is \(\mathrm{PV}^{3 / 2}\). The initial temperature of the gas is '\(\mathrm{T}\)'. When the gas is compressed to half of its Initial volume, the final temperature of the gas ...

A perfect gas of volume 10 litre n compressed isothermally to a volume of 1 litre. The rms speed of the molecules will

The root mean square velocity of molecules of a gas is $200 \mathrm{~m} / \mathrm{s}$. What will be the root mean square velocity of the molecules, if the molecular weight is doubled and the absolute temperature is halved?

A monoatomic gas of pressure \(p\) having volume \(V\) expands isothermally to a volume \(2V\) and then adiabatically to a volume \(16 \mathrm{~V}\). The final pressure of the gas is (ratio of specific heats \(=\frac{5}{3}\)

For a gas, \(\frac{R}{C_V}=0.4\), where \(R\) is universal gas constant and \(C_V\) is the molar specific heat at constant volume. The gas is made up of molecules, which are

A diatomic gas undergoes adiabatic change. Its pressure \(p\) and temperature \(T\) are related as \(p \propto T^x\), where \(x\) is

Two spherical black bodies of radius \(r_1\) and \(r_2\) with surface temperature \(T_1\) and \(T_2\) respectively, radiate same power, then \(r_1: r_2\) is

The rms speed of oxygen molecule in a gas is $u$, If the temperature is doubled and the molecules dissociates into two atoms, the rms speed will be

The SI unit and dimensions of Stefan's constant $\sigma$ in case of Stefan's law of radiation is

A clock pendulum having coefficient of linear expansion. $\alpha=9 \times 10^{-7} /{ }^{\circ} \mathrm{C}^{-1}$ has a period of 0.5 s at $20^{\circ} \mathrm{C}$. If the clock is used in a climate, where the temperature is $30^{\circ} \mathr...

If $\alpha$ is the coefficient of performance of a refrigerator and ' $Q$ ' is heat released to the hot reservoir, then the heat extracted from the cold reservoir ' $Q_2$ ' is

If ' $C_P$ ' and ' $C_V$ ' are molar specific heats of an ideal gas at constant pressure and volume respectively. If ' $\lambda$ ' is the ratio of two specific heats and ' $R$ ' is universal gas constant then ' $C_p$ ' is equal to

The maximum wavelength of radiation emitted by a star is 289.8 nm . Then intensity of radiation for the star is (Given : Stefan's constant $=5.67 \times 10^{-8} \mathrm{Wm}^{-2} \mathrm{~K}^{-4}$, Wien's constant, $b=2898 \mu \mathrm{mK}$ )

The equation of state for 2 g of oxygen at a pressure ' $P$ ' and temperature ' $T$, when occupying a volume ' $V$ ' will be