If the RMS velocity of an ideal gas is v ms^ | vedclass

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

Question

(C) The root mean square $(RMS)$ velocity of an ideal gas is given by the formula: $v_{rms} = \sqrt{\frac{3RT}{M}}$.Since $v_{rms} \propto \sqrt{T}$,w

Vedclass · Accepted Answer

$1600$

Vedclass · Answer

(C) The root mean square $(RMS)$ velocity of an ideal gas is given by the formula: $v_{rms} = \sqrt{\frac{3RT}{M}}$.Since $v_{rms} \propto \sqrt{T}$,we can write: $\frac{v_1}{v_2} = \sqrt{\frac{T_1}{T_2}}$.Given $T_1 = 127^{\circ} C = 127 + 273 = 400 \ K$ and $v_1 = v$.We want to find $T_2$ such that $v_2 = 2v$.Substituting the values: $\frac{v}{2v} = \sqrt{\frac{400}{T_2}}$.$\frac{1}{2} = \sqrt{\frac{400}{T_2}}$.Squaring both sides: $\frac{1}{4} = \frac{400}{T_2}$.$T_2 = 400 	imes 4 = 1600 \ K$.

If the $RMS$ velocity of an ideal gas is $v \ ms^{-1}$ at $127^{\circ} C$,at what temperature its $RMS$ velocity is doubled (in $K$)?

Similar Questions

The most probable speed of $O_2$ molecules at $T \ K$ is

At what temperature $(^o C)$ will the $rms$ speed of $CO_2$ be equal to the $rms$ speed of $CO$ at $STP$?

The r.m.s. velocity of $CO_2$ at a temperature $T$ (in kelvin) is $x \ cm \ s^{-1}$. At what temperature (in kelvin),the r.m.s. velocity of nitrous oxide would be $4 x \ cm \ s^{-1}$ (in $T$)? (Atomic weights of $C, N$ and $O$ are respectively $12, 14$ and $16$)

Which of the following changes can be made in order to double the root mean square speed,$(V_{rms})$,of a gas kept in a rigid container?

Explain the relationship between different types of molecular speeds.

Vedclass Test Series

Exam Paper Generator

Online Exam Module