Let bar{v},v_{rms} and v_p respectively denot | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) The expressions for the speeds are:$v_{rms} = \sqrt{\frac{3kT}{m}}$$\bar{v} = \sqrt{\frac{8kT}{\pi m}} \approx \sqrt{\frac{2.55kT}{m}}$$v_p = \sqr

Vedclass · Accepted Answer

the average kinetic energy of the molecules is $\frac{3}{4}(mv_p^2)$

Vedclass · Answer

(D) The expressions for the speeds are:$v_{rms} = \sqrt{\frac{3kT}{m}}$$\bar{v} = \sqrt{\frac{8kT}{\pi m}} \approx \sqrt{\frac{2.55kT}{m}}$$v_p = \sqrt{\frac{2kT}{m}}$Comparing these,we get $v_p For the average kinetic energy of a molecule:$E_k = \frac{1}{2} m v_{rms}^2 = \frac{1}{2} m \left( \sqrt{\frac{3kT}{m}} \right)^2 = \frac{3}{2} kT$.Since $v_p^2 = \frac{2kT}{m}$,we have $kT = \frac{1}{2} m v_p^2$.Substituting this into the expression for $E_k$:$E_k = \frac{3}{2} \left( \frac{1}{2} m v_p^2 \right) = \frac{3}{4} m v_p^2$.

Let $\bar{v}$,$v_{rms}$ and $v_p$ respectively denote the mean speed,root mean square speed and most probable speed of the molecules in an ideal monoatomic gas at absolute temperature $T$. The mass of the molecule is $m$. Then:

Similar Questions

At a given temperature,which gas has a higher speed: light or heavy?

If the $rms$ speed of oxygen molecules at $0^{\circ} {C}$ is $160 \; {m/s}$,find the $rms$ speed of hydrogen molecules at $0^{\circ} {C}$ (in ${m/s}$).

The root mean square velocity of a gas molecule of mass $m$ at a given temperature is proportional to

The molecules of a given mass of a gas have $r.m.s.$ velocity of $200 \,m s^{-1}$ at $27^o C$ and $1.0 \times 10^5 \,N m^{-2}$ pressure. When the temperature and pressure of the gas are respectively $127^o C$ and $0.05 \times 10^5 \,N m^{-2},$ the $r.m.s.$ velocity of its molecules in $m s^{-1}$ is

When pressure remains constant,at what temperature will the $r.m.s.$ speed of gas molecules increase by $10 \%$ of the $r.m.s.$ speed at $STP$?

Vedclass Test Series

Exam Paper Generator

Online Exam Module