Two closed containers of equal volume are filled with air at pressure ${\mathrm{P}}_0$ and temperature ${\mathrm{T}}_0$. Both are connected by a narrow tube. If one of the containers is maintained at temperature ${\mathrm{T}}_0$ and the other at temperature T, then new pressure in the container will be:

1. $\frac{2{\mathrm{P}}_0\mathrm{T}}{\mathrm{T}+{\mathrm{T}}_0}$

2. $\frac{{\mathrm{P}}_0\mathrm{T}}{\mathrm{T}+{\mathrm{T}}_0}$

3. $\frac{{\mathrm{P}}_0\mathrm{T}}{2(\mathrm{T}+{\mathrm{T}}_0)}$

4. $\frac{\mathrm{T}+{\mathrm{T}}_0}{{\mathrm{P}}_0}$

The ratio of the average translatory kinetic energy of He gas molecules to ${\mathrm{O}}_2$ gas molecules is:

1. $\frac{25}{21}$

2. $\frac{21}{25}$

3. $\frac{3}{2}$

4. 1

Heat is  associated with:

The rms speed of the molecules of an enclosed gas is \(v\). What will be the rms speed if the pressure is doubled, keeping the temperature constant?

What is the average thermal energy of a helium atom at room temperature (\(27^{\circ}\mathrm{C}\))?

When an ideal gas is compressed adiabatically, its temperature rises: the molecules on an average have more kinetic energy than before. The kinetic energy increases:

1 mole of an ideal gas is contained in a cubical volume V, ABCDEFGH at 300 K (figure). One face of the cube (EFGH) is made up of a material which totally absorbs any gas molecule incident on it. At any given time:
                               

Diatomic molecules like hydrogen have energies due to both translational as well as rotational motion. From the equation in kinetic theory, \(PV = \frac{2}{3}E\)$,$ \(E\) is:

The graph between volume and temperature in Charle's law is?
1. an ellipse
2. a circle
3. a straight line
4. a parabola

The mean free path for a gas, with molecular diameter \(d\) and number density \(n,\) can be expressed as:
1. \( \frac{1}{\sqrt{2} n \pi \mathrm{d}^2} \)
2. \( \frac{1}{\sqrt{2} n^2 \pi \mathrm{d}^2} \)
3. \(\frac{1}{\sqrt{2} n^2 \pi^2 d^2} \)
4. \( \frac{1}{\sqrt{2} n \pi \mathrm{d}}\)