Interstellar space (far from any stars) contains atomic hydrogen (H) with a density of 1 atom/cm3 and at a temperature of about 2.7 K. Determine (a) the pressure in interstellar…

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asked Nov 23, 2020 120k views

1 Answer

Vivian · Answer 1 · 2020-11-30T03:14:51+0000

Step-by-step explanation:

Given that,

Number density
$n= 1\ atom/cm^(3) =10^(6)\ atom/m^3$

Temperature = 2.7 K

(a). We need to calculate the pressure in interstellar space

Using ideal gas equation

PV=nRT

P=(nRT)/(V)

P=(10^(6)*8.314*2.7)/(6.023*10^(23))

$P=3.727*10^(-17)\ Pa$

$P=36.78*10^(-23)\ atm$

The pressure in interstellar space is
$36.78*10^(-23)\ atm$

(b). We need to calculate the root-mean square speed of the atom

Using formula of rms

$v_(rms)=\sqrt{(3RT)/(Nm)}$

Put the value into the formula

$v_(rms)=\sqrt{(3*8.314*2.7)/(1.007*10^(-3))}$

$v_(rms)=258.6\ m/s$

The root-mean square speed of the atom is 258.6 m/s.

(c). We need to calculate the kinetic energy

Average kinetic energy of atom

E=(3)/(2)kT

Where, k = Boltzmann constant

Put the value into the formula

E=(3)/(2)*1.38*10^(-23)*2.7

$E=5.58*10^(-23)\ J$

The kinetic energy stored in 1 km³ of space is
$5.58*10^(-23)\ J$ .

Hence, This is the required solution.