Further if the vessel now thermally insulated moved with a constant speed v and then suddenly stopped results in a rise of temperature of $2^{\circ} C$ , Find v

Open in App

Solution

RMS velocity is given by the formula

$v_{r m s} = \sqrt{\frac{3 R T}{M}}$

In the two cases, effective velocity will differ by v.

Hence,

$v = \sqrt{\frac{3 R (T + 2)}{M}} - \sqrt{\frac{3 R T}{M}}$

Since $T >> 2$ ,

$v = \sqrt{\frac{3 R T}{M}} (\sqrt{1 + \frac{2}{T}}) - \sqrt{\frac{3 R T}{M}} \approx \sqrt{\frac{3 R T}{M}} (1 + \frac{1}{T}) - \sqrt{\frac{3 R T}{M}} = \sqrt{\frac{3 R}{M T}}$

$v \approx 3 m / s$

Answer is $3 m / s$

Suggest Corrections

Similar questions

Q. One mole of oxygen at

27^{o}

C and at one atmospheric pressure is enclosed in a vessel. The vessel is now thermally insulated and moved with a constant speed

V_{0}

. It is then suddenly stopped. The process results in a rise of the temperature of the gas by

1^{o}

C. Calculate the speed

V_{0}

Q. One gram mole of oxygen is enclosed in a vessel at a temperature of

27

and at one atmospheric pressure. The vessel is thermally insulated and is moved with a constant speed

u_{0}

. Calculate

u_{0}

if the rise in temperature is

1 K

when the vessel is suddenly stopped?

Q. An insulated box containing a diatomic gas of molecular mass

M

is moving with velocity

v

. If the box is suddenly stopped, the resulting change in temperature is (

R

is the gas constant)

An insulated box containing a diatomic gas of molar mass $M$ is moving with a velocity $v$ . If the box is suddenly stopped, the resulting change in temperature is ( $R$ is the gas constant)

Q. Certain amount of an ideal gas of molecular mass M is contained in a closed vessel. If the vessel is moving with a constant velocity v, then the rise in temperature of the gas when the vessel is suddenly stopped will be
(Take

γ = \frac{C_{P}}{C_{V}}

)

Join BYJU'S Learning Program

Further if the vessel now thermally insulated moved with a constant speed v and then suddenly stopped results in a rise of temperature of 2∘C, Find v

RMS velocity is given by the formulavrms=√3RTMIn the two cases, effective velocity will differ by v.Hence,v=√3R(T+2)M−√3RTMSince T>>2,v=√3RTM(√1+2T)−√3RTM≈√3RTM(1+1T)−√3RTM=√3RMTv≈3m/sAnswer is 3m/s

Further if the vessel now thermally insulated moved with a constant speed v and then suddenly stopped results in a rise of temperature of $2^{\circ} C$ , Find v