Answer:
T=183.21K
Explanation:
We have to take into account that the system is a ideal gas. Hence, we have the expression
[tex]PV=nRT[/tex]
where P is the pressure, V is the volume, n is the number of moles, T is the temperature and R is the ideal gas constant.
Thus, it is necessary to calculate n and V
V is the volume of a sphere
[tex]V=\frac{4}{3}\pi r^3=\frac{4}{3}\pi (5.9*10^{15}m)^3=8.602*10^{47}m^3[/tex]
V=8.86*10^{50}L
and for n
[tex]n=\frac{(4000M_s)/(2*mH)}{6.022*10^{23}mol^{-1}}=3.95*10^{36}mol[/tex]
Hence, we have (1 Pa = 9.85*10^{-9}atm)
[tex]T=\frac{PV}{nR}=\frac{(6.8*10^{-9}*9.85*10^{-6}atm)(8.86*10^{50}L)}{(0.0820\frac{atm*L}{mol*K})(3.95*10^{36}mol)}\\\\T=183.21K[/tex]
hope this helps!!
