A gas mixture consists of molecules of type 1, 2 and 3, with molar masses ${\mathrm{m}}_1>{\mathrm{m}}_2>{\mathrm{m}}_3. {\mathrm{V}}_{\mathrm{rms}}$ and $\overline{\mathrm{K}}$ are the r.m.s. speed and average kinetic energy of the gases. Which of the following is true

Two ideal gases at absolute temperature ${\mathrm{T}}_1$ and ${\mathrm{T}}_2$ are mixed. There is no loss of energy. The masses of the molecules are ${\mathrm{m}}_1$ and ${\mathrm{m}}_2$ and the number of molecules in the gases are ${\mathrm{n}}_1$ and ${\mathrm{n}}_2$ respectively. The temperature of mixture will be

The molecules of an ideal gas at a certain temperature have

The temperature at which the average translational kinetic energy of a molecule is equal to the energy gained by an electron in accelerating from rest through a potential difference of 1 volt is

N molecules each of mass m of gas A and 2N molecules each of mass 2m of gas B are contained in the same vessel at temperature T. The mean square of the velocity of molecules of gas B is ${\mathrm{v}}^2$ and the mean square of x component of the velocity of molecules of gas A is ${\mathrm{w}}^2$. The ratio is $\frac{{\mathrm{w}}^2}{{\mathrm{v}}^2}$is

A gas is filled in a cylinder, its temperature is increased by 20% on Kelvin scale and volume is reduced by 10%. How much percentage of the gas will leak out: (Assume pressure is constant)

The air density at Mount Everest is less than that at the sea level. It is found by mountaineers that for one trip lasting a few hours, the extra oxygen needed by them corresponds to 30,000 cc at sea level (pressure 1 atmosphere, temperature 27°C). Assuming that the temperature around Mount Everest is –73°C and that the oxygen cylinder has capacity of 5.2 litre, the pressure at which ${\mathrm{O}}_2$ be filled (at site) in cylinder is

$\frac{1}{2}$ mole of helium gas is contained in a container at S.T.P. The heat energy needed to double the pressure of the gas, keeping the volume constant (specific heat of the gas $=3 \mathrm{J} {\mathrm{gm}}^{-1} {\mathrm{K}}^{-1}$) is 

The equation of state of a gas is given by $\left(\mathrm{P}+\frac{{\mathrm{aT}}^2}{\mathrm{V}}\right){\mathrm{V}}^{\mathrm{c}}=\left(\mathrm{RT}+\mathrm{b}\right),$ where a, b, c and R are constants. The isotherms can be represented by $\mathrm{P}={\mathrm{AV}}^{\mathrm{m}}-{\mathrm{BV}}^{\mathrm{n}},$ where A and B depend only on temperature and 

70 calories of heat is required to raise the temperature of 2 moles of an ideal gas at constant pressure from 30°C to 35°C. The amount of heat required to raise the temperature of same gas through the same range (30°C to 35°C) at constant volume (R = 2 cal/mol/K)

A closed compartment containing gas is moving with some acceleration in horizontal direction. Neglect effect of gravity. Then the pressure in the compartment is

Three closed vessels A, B and C are at the same temperature T and contain gases which obey the Maxwellian distribution of velocities. Vessel A contains only ${\mathrm{O}}_2 , \mathrm{B}$ only ${\mathrm{N}}_2$ and C a mixture of equal quantities of ${\mathrm{O}}_2$ and ${\mathrm{N}}_2$. If the average speed of the ${\mathrm{O}}_2$ molecules in vessel A is ${\mathrm{V}}_1 ,$ that of the ${\mathrm{N}}_2$ molecules in vessel B is ${\mathrm{V}}_2 ,$ the average speed of the ${\mathrm{O}}_2$ molecules in vessel C is

A box containing N molecules of a perfect gas at temperature ${\mathrm{T}}_1$ and pressure ${\mathrm{P}}_1$. The number of molecules in the box is doubled keeping the total kinetic energy of the gas same as before. If the new pressure is ${\mathrm{P}}_2$ and temperature ${\mathrm{T}}_2$, then

Two identical glass bulbs are interconnected by a thin glass tube. A gas is filled in these bulbs at N.T.P. If one bulb is placed in ice and another bulb is placed in hot bath, then the pressure of the gas becomes 1.5 times. The temperature of hot bath will be

Two containers of equal volumes contain the same gas at pressures ${\mathrm{P}}_1$ and ${\mathrm{P}}_2$ and absolute temperatures ${\mathrm{T}}_1$ and ${\mathrm{T}}_2$, respectively. On joining the vessels, the gas reaches a common pressure P and common temperature T. The ratio P/T is equal to

Which one, of the following, graphs represents the behaviour of an ideal gas at constant temperature?

A closed vessel contains 8gm of oxygen and 7gm of nitrogen. The total pressure is 10 atm at a given temperature. If now oxygen is absorbed by introducing a suitable absorbent the pressure of the remaining gas in atm will be

${\mathrm{CO}}_2\left(\mathrm{O}=\mathrm{C}=\mathrm{O}\right)$ is a triatomic gas. Mean kinetic energy of one gram gas will be (If N-Avogadro's number, k-Boltzmann's constant and molecular weight of ${\mathrm{CO}}_2=44$ , Degree of freedom f = 7)

40 calories of heat is needed to raise the temperature of 1 mole of an ideal monoatomic gas from 20°C to 30°C at a constant pressure. The amount of heat required to raise its temperature over the same interval at a constant volume $\left(\mathrm{R}=2 \mathrm{calorie} {\mathrm{mole}}^{-1} {\mathrm{K}}^{-1}\right)$ is

The pressure and volume of saturated water vapour are P and V respectively. It is compressed isothermally thereby volume becomes V/2, the final pressure will be

If the intermolecular forces vanish away, the volume occupied by the molecules contained in 4.5 kg water at standard temperature and pressure will be

When an air bubble of radius ‘r’ rises from the bottom to the surface of a lake, its radius becomes 5r/4 (the pressure of the atmosphere is equal to the 10 m height of water column). If the temperature is constant and the surface tension is neglected, the depth of the lake is

A horizontal uniform glass tube of 100 cm, length sealed at both ends contain 10 cm mercury column in the middle. The temperature and pressure of air on either side of mercury column are respectively 81°C and 76 cm of mercury. If the air column at one end is kept at 0°C and the other end at 273°C, the pressure of air which is at 0°C is (in cm of Hg)

At standard temperature and pressure the density of a gas is $1.3 \mathrm{kg}/{\mathrm{m}}^3$ and the speed of the sound in gas is 330 m/sec. Then the degree of freedom of the gas will be

The temperature of 5 moles of a gas which was held at constant volume was changed from $100°\mathrm{C}$ to $120°\mathrm{C}$. The change in internal energy was found to be 80 Joules. The total heat capacity of the gas at constant volume will be equal to

The temperature at which the r.m.s. speed of hydrogen molecules is equal to escape velocity on earth surface, will be

Inside a cylinder having insulating walls and closed at ends is a movable piston, which divides the cylinder into two compartments. On one side of the piston is a mass m of a gas and on the other side a mass 2 m of the same gas. What fraction of volume of the cylinder will be occupied by the larger mass of the gas when the piston is in equilibrium ? Consider that the movable piston is conducting so that the temperature is the same throughout

The diameter of oxygen molecules is $2.94\times {10}^{-10} \mathrm{m}.$ The Vander Waal's gas constant 'b' in ${\mathrm{m}}^3/\mathrm{mol}$ will be

The temperature of the mixture of one mole of helium and one mole of hydrogen is increased from $0°\mathrm{C}$ to $100°\mathrm{C}$ at constant pressure. The amount of heat delivered will be

A vessel contains a mixture of one mole of oxygen and two moles of nitrogen at 300 K. The ratio of the average rotational kinetic energy per ${\mathrm{O}}_2$ molecule to that per ${\mathrm{N}}_2$ molecule is