Question

Which of the following expression correctly
represents the change in root mean square velocity if the temperature of gas
of a gas (mol. mass = M) changes by deltaT?

*Please post with solution*

Answer 1

we have to check that which of the given expression correctly represents the change in root mean square velocity if the temperature of gas change by ∆T.

solution : root mean square velocity is given by,

v = √(3RT/M)

where T is temperature and M is molecular mass of gas.

now differentiating v with respect to T.

dv/dT = d{√(3RT/M)}/dT

⇒dv/dT = 1/2√(3RT/M) × 3R/M dT/dT

⇒dv/dT = 1/2v × 3R/M

⇒∆v/∆T = 3R/2Mv

⇒∆v = 3R∆T/2Mv

Therefore the change in root mean square velocity is given by , $\frac{3R\Delta T}{2Mv_{rms}}$