At a temperature of 27^{circ}C and a pressure | vedclass

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

Question

(C) The $rms$ speed of a gas is given by the formula $v_{rms} = \sqrt{\frac{3RT}{M}}$.From this,we can see that $v_{rms} \propto \sqrt{T}$.Note that t

Vedclass · Accepted Answer

$\frac{400}{\sqrt{3}} \, m/s$

Vedclass · Answer

(C) The $rms$ speed of a gas is given by the formula $v_{rms} = \sqrt{\frac{3RT}{M}}$.From this,we can see that $v_{rms} \propto \sqrt{T}$.Note that the $rms$ speed is independent of the pressure of the gas.Given: $T_1 = 27^{\circ}C = 27 + 273 = 300 \, K$ and $v_1 = 200 \, m/s$.Given: $T_2 = 127^{\circ}C = 127 + 273 = 400 \, K$.Using the proportionality $v_1 / v_2 = \sqrt{T_1 / T_2}$:$\frac{200}{v_2} = \sqrt{\frac{300}{400}} = \sqrt{\frac{3}{4}} = \frac{\sqrt{3}}{2}$.Therefore,$v_2 = \frac{200 	imes 2}{\sqrt{3}} = \frac{400}{\sqrt{3}} \, m/s$.

At a temperature of $27^{\circ}C$ and a pressure of $1.0 \times 10^5 \, N/m^2$,the $rms$ speed of a gas is $200 \, m/s$. What is the $rms$ speed at a temperature of $127^{\circ}C$ and a pressure of $0.5 \times 10^5 \, N/m^2$?

Similar Questions

What is the ${v_{rms}}$ of gas molecules in equilibrium?

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

The velocities of $4$ gas molecules are given by $1 \ km/s, 3 \ km/s, 5 \ km/s$ and $7 \ km/s$. Calculate the difference between the average velocity and the root mean square $(RMS)$ velocity. (in $km/s$)

For a mixture of three different gases with molecular masses $m_1 > m_2 > m_3$ at the same temperature,what is the relationship between their root mean square speeds $(v_{rms})$ and average kinetic energies $(\bar{K})$?

The ratio of $r.m.s.$ velocities of oxygen and hydrogen at a given temperature is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module