Question

The root mean square speed of an unknown gas at 27 C is 'x'cm/s.
The temperature at which
its rms speed will be 3 cm/s, is ?​

Answer 1

Answer:

rms speed of the gas will be:

A .

9×104cm/s

B .

3×104cm/s

C .

3×104cm/s

D .

1×104cm/s

December 20, 2019avatarAdwitiyaa Dey

Answer

Given,

RMS of molecules urms=104cm/sec

Pressure initially =1.5bar

Temperature T1=27K

Now,we know

Temperature T2=2×27K

Pressure P2=2×1.5bar

Also,

urms=M3RT

It is evident that urms is not affected by pressure.ONly change in temperature will affect.

Now,

urms2urms1=M3RT2M3RT1

urms2urms1=T2T1

urms2104=5427

urms2=1.7×104m/s

Answer 2

The temperature would be $T_2={\frac{2700}{x^2}}$°C.

Explanation:

The root mean square speed $v_{rms} =\sqrt{\frac{3RT}{M}}$

Since the gas is unknown, we don't know what is the value of M in the equation.

But, the question says, root mean square speed of an unknown gas at 27 °C is 'x'cm/s. So, v1 = x cm/s, T1 = 27 °C = 273 + 27 = 300 K

Case 2: v2 = 3cm/s, T2 = T2(unknown)

So, we can rearrange the above formula, such that only the terms T and v are left, such that,

$\frac{v_1}{v_2} =\sqrt{\frac{T_1}{T_2}}$

$\frac{x}{3} =\sqrt{\frac{300}{T_2}}$

$(\frac{x}{3})^2 ={\frac{300}{T_2}}$

$T_2={\frac{300\times 9}{x^2}}$

$T_2={\frac{2700}{x^2}}$