Respuesta :
Explanation:
Given that,
Number density [tex]n= 1\ atom/cm^{3} =10^{6}\ atom/m^3[/tex]
Temperature = 2.7 K
(a). We need to calculate the pressure in interstellar space
Using ideal gas equation
[tex]PV=nRT[/tex]
[tex]P=\dfrac{nRT}{V}[/tex]
[tex]P=\dfrac{10^{6}\times8.314\times2.7}{6.023\times10^{23}}[/tex]
[tex]P=3.727\times10^{-17}\ Pa[/tex]
[tex]P=36.78\times10^{-23}\ atm[/tex]
The pressure in interstellar space is [tex]36.78\times10^{-23}\ atm[/tex]
(b). We need to calculate the root-mean square speed of the atom
Using formula of rms
[tex]v_{rms}=\sqrt{\dfrac{3RT}{Nm}}[/tex]
Put the value into the formula
[tex]v_{rms}=\sqrt{\dfrac{3\times8.314\times2.7}{1.007\times10^{-3}}}[/tex]
[tex]v_{rms}=258.6\ m/s[/tex]
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
[tex]E=\dfrac{3}{2}kT[/tex]
Where, k = Boltzmann constant
Put the value into the formula
[tex]E=\dfrac{3}{2}\times1.38\times10^{-23}\times2.7[/tex]
[tex]E=5.58\times10^{-23}\ J[/tex]
The kinetic energy stored in 1 km³ of space is [tex]5.58\times10^{-23}\ J[/tex].
Hence, This is the required solution.
