Download App

Kinetic Theory of Gases and Radiation — Physics STD 12 Science — Question

Maharashtra BoardEnglish MediumSTD 12 SciencePhysicsKinetic Theory of Gases and Radiation3 Marks
Question
At what temperature will helium molecules have the same rms speed as that of hydrogen molecules at STP ? (Molar mass of hydrogen $=2 \mathrm{~g} / \mathrm{mol}$, molar mass of helium $=4 \mathrm{~g} / \mathrm{mol}$ )
✓

Answer


Data : $M_{01}$ (hydrogen) $=2 \mathrm{~g} / \mathrm{mol}$
$\mathrm{M}_{02}$ (helium) $=4 \mathrm{~g} / \mathrm{mol}, \mathrm{T}_1$ (hydrogen) $=273 \mathrm{~K}$,
$v_{\text {rms }}$ (hydrogen) $=v_{2 \mathrm{rms}}$ (helium)
$v_{\text {rms }}=\sqrt{\frac{3 R T}{M_0}} \quad$ MaharashtraBoardSolutions.Guru
$\therefore v_{1 \mathrm{rms}}=\sqrt{\frac{3 R T_1}{M_{01}}}$ and $v_{2 \mathrm{rms}}=\sqrt{\frac{3 R T_2}{M_{02}}}$
Now, $v_{1 \mathrm{rms}}=v_{2 \mathrm{rms}} \quad \therefore \frac{T_1}{M_{01}}=\frac{T_2}{M_{02}}$
$
\therefore T_2=T_1 \frac{M_{02}}{M_{01}}=273 \times \frac{4}{2}=546 \mathrm{~K}
$
The temperature of helium $=546 \mathrm{~K}=273^{\circ} \mathrm{C}$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "Answer the following in Brief" from Kinetic Theory of Gases and Radiation→Kinetic Theory of Gases and Radiation — all question types→Physics STD 12 Science question papers→Maharashtra Board STD 12 Science question papers→Maharashtra Board question paper generator→

Similar questions

Obtain an expression for the energy stored in a charged condenser. Express it in different forms.
→
If the frequency of revolution of a proton $\left( q =1.6 \times 10^{-19} C \right)$ in a uniform magnetic induction is $10^6 \ Hz,$ what is the corresponding electric current?
→
Suppose a dam is $250 \mathrm{~m}$ wide and the water is $40 \mathrm{~m}$ deep at the dam. What is
(i) the average pressure on the dam
(ii) the force exerted against the dam due to the water?
→
The magnetic field at the centre of a circular loop of radius $12.3\ cm$ is $6.4 \times 10^{-6} T$. What will be the magnetic moment of the loop?
→
How does the frequency of an SHM vary with
1. the force constant $k$
2. the mass of the particle performing SHM ?
→
Obtain expressions of energy of a particle at different positions in the vertical circular motion.
→
A body of surface area $400 \mathrm{~cm}^2$ and absorption coefficient 0.5 radiates energy $1.5 \mathrm{kcal}$ in 2 minutes when the temperature of the body is kept constant. Find the temperature of the body. (Given : J = $4186 \mathrm{~J} / \mathrm{kcal}, \sigma=5.67 \times 10^{-8} \mathrm{~J} / \mathrm{s} \cdot \mathrm{m} \cdot \mathrm{K}^4$ )
→
The refractive index of a medium is $\sqrt{3}$. What is the angle of refraction, if the unpolarized light is incident on it at the polarizing angle of the medium?
→
Derive an expression for kinetic energy of a rotating body.
→
In a Wheatstone’s meter-bridge experiment, the null point is obtained in middle one third portion of wire. Why is it recommended?
→