Question

Can pockets of vacuum persist in an ideal gas? Assume that a room is filled with air at 20∘C and that somehow a small spherical region of radius 1 cm within the room becomes devoid of air molecules. Estimate how long it will take for air to refill this region of vacuum. Assume the atomic mass of air is 29 u.

Answer 1

Answer:

time taken is 20 μs

Explanation:

given data

temperature = 20°C  = 293 K

radius = 1 cm

atomic mass of air = 29 u

to find out

how long it will take for air to refill

solution

we find here rms velocity of air particle that is

$\frac{1}{2}mv^2 = \frac{3}{2}RT$

here m is mass and t is temperature and v is speed and R is ideal gas constant i.e. 8.3145 (kg·m²/s²)/K·mol

v = $\sqrt{\frac{3RT}{M} }$  ............................1

v = $\sqrt{\frac{3(8.314)293}{29*10{-3}kg} }$

v = 501.99 m/s

so now for cover 1 cm

time taken by air

time take = $\frac{r}{v}$

time taken = $\frac{1*10^{-2}m}{501.99}$

time taken = 19.92 × $10^{6}$ s = 20μs

so time taken is 20 μs