Download App

Kinetic Theory — Physics STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 SciencePhysicsKinetic Theory5 Marks
Question
A gaseous mixture contains $16g$ of helium and $16g$ of oxygen, then calculate the ratio of $\frac{\text{C}_{\text{p}}}{\text{C}_{\text{V}}}$ of the mixture.
✓

Answer

Moles of helium $(\mu_{\text{He}})=\frac{16}{4}=4$ Moles of oxygen $(\mu_{\text{O}_2})=\frac{16}{32}=\frac{1}{2}$As helium is monoatomic, so degrees of freedom of helium, f = 3, so $\text{C}_{\text{V}_{\text{He}}}=\frac{\text{f}}{2}\text{R}=\frac{3}{2}\text{R}$
As oxygen is diatomic, so degrees of freedom of oxygen f = 5, so$\text{C}_{\text{V}_{\text{O}_2}}=\frac{\text{f}}{2}\text{R}=\frac{5}{2}\text{R}$
$\therefore\text{C}_{\text{V mixture}}=\frac{\mu_{\text{He}}\text{C}_{\text{V}_{\text{He}}}+\mu_{\text{O}_2}\text{C}_{\text{V}_{\text{O}_2}}}{\mu_{\text{He}}+\mu\text{O}_2}$
$=\frac{4\times\frac{3}{2}\text{R}+\frac{1}{2}\times\frac{5}{2}\text{R}}{4+\frac{1}{2}}=\frac{29}{18}\text{R}$
$\gamma=\frac{\text{C}_{\text{P}}}{\text{C}_{\text{V}}}$ [of mixture]
$\gamma_{\text{mixture}}=1+\frac{\text{R}}{\text{C}_{\text{V}_{\text{mixture}}}}$
$=1+\frac{\text{R}}{\frac{29}{18}\text{R}}=1.62$ [as $C_P - C_V = R$]

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 "5 Marks Questions" from Kinetic Theory→Kinetic Theory — all question types→Physics STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

For the wave on a string described in Exercise 15.11, do all the points on the string oscillate with the same,
  1. Frequency,
  2. Phase,
  3. Amplitude?
→
A geostationary satellite is orbiting the earth at a height of 6R above the surface of earth. Here R is the radius of the earth. What is the time period of another satellite at a height of 2.5R from the surface of the earth?
→
The coil of an electric bulb takes 40 watts to start glowing. If more than 40W is supplied, 60% of the extra power is converted into light and the remaining into heat. The bulb consumes 100W at 220V. Find the percentage drop in the light intensity at a point if the supply voltage changes from 220V to 200V.
→
A capacitor of capacitance C is connected to a battery of emf $\in$ at t = 0 through a resistance R. Find the maximum rate at which energy is stored in the capacitor. When does the rate have this maximum value?
→
Position $x$, time of particle moving in onedimensional motion depends on as follows :
$x=5+5 t-t^2$
(All quantities are in SI units) For this motion draw (i) displacement-time (ii) Velocity-time (iii) Acceleration-time graphs for the time interval $t=0 sec$ to $t=6 sec$ and describe the motion.
→
Describe surface tension on the basis of molecular forces.
→
An inductor-coil of resistance $10\Omega$ and induetanes 120mH is connected across a battery of emf 6V and Internal resistance $2\Omega.$ Find the charge which flows through the inductor in:
  1. 10ms
  2. 20ms
  3. 100 ms after the connections are made.
→
Read statement below carefully and state with reasons and examples, if it is true or false; A particle in one-dimensional motion. With positive value of acceleration must be speeding up.
→
Explain the experimental demonstration of in- terference by making a labelled diagram of a quinke tube.
→
The motion of a particle executing simple harmonic motion is described by the displacement function, $x ( t )= A \cos (\omega t$ $+\phi)$ If the initial $(t=0)$ position of the particle is 1 cm and its initial velocity is $\omega cm / s$, then what are its amplitude and initial phase angle? The angular frequency of the particle is $\pi s ^{-1}$. If instead of the cosine function, we choose the sine function to describe the $SHM , x = B \sin (\omega t +\phi)$, then what are the amplitude and initial phase of the particle with the above initial conditions?
→