At NTP, sample of equal volume of chlorine and oxygen is taken. Now ratio of no. of molecules is

At ${0^ \circ }C$ the density of a fixed mass of a gas divided by pressure is $x.$ At ${100^ \circ }C,$ the ratio will be

The pressure and temperature of two different gases is $P$ and $T$ having the volume $V$ for each. They are mixed keeping the same volume and temperature, the pressure of the mixture will be

In the nuclear fusion reaction

${}_1^2{\rm{H}}\,\, + \,\,{}_1^3{\rm{H}} o {}_2^4{\rm{H}}e\,\, + \,\,n$

given that the repulsive potential energy between the two nuclei is $7.7\,\, imes \,\,{10^{ - 14}}{\rm{ J}}$, the temperature at which the gases must be heated to initiate the reaction is nearly [Boltzmann’s constant $k = 1.38\,\, imes \,\,{10^{ - 23}}\,\,{\rm{J}}{{\rm{K}}^{ - 1}}$]

The mean free path for ${\rm{a}}$ gas, with molecular diameter ${\rm{d}}$ and number density ${\rm{n}}$ can be expressed as:

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

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

Two gases $A$ and $B$ having same pressure $p$, volume $V\;$ and absolute temperature $T$ are mixed. If the mixture has the volume and temperature as $V$ and $T$ respectively, then the pressure of the mixture is

The de-Broglie wavelength of a neutron in thermal equilibrium with heavy water at a temperature $T$ (Kelvin) and mass $m$, is

Read the given statements and decide which is/are correct on the basis of kinetic theory of gases

(I) Energy of one molecule at absolute temperature is zero

(II) $r.m.s.$speeds of different gases are same at same temperature

(III) For one gram of all ideal gas kinetic energy is same at same temperature

(IV) For one mole of all ideal gases mean kinetic energy is same at same temperature

A gas undergoes a process where its pressure increases linearly with volume, $P = aV + b$, where $a$ and $b$ are positive constants. If the initial volume is $V_0$ and the final volume is $2V_0$, what is the work done by the gas during this process?