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viva [34]
3 years ago
7

The Orion nebula is one of the brightest diffuse nebulae in the sky (look for it in the winter, just below the three bright star

s in Orion's belt). It is a very complicated mess of gas, dust, young star systems, and brown dwarfs, but let's estimate its temperature if we assume it is a uniform ideal gas. Assume it is a sphere of radius r = 5.9 × 1015 m (around 6 light years) with a total mass 4000 times the mass of the Sun. If the gas is all diatomic hydrogen and the pressure in the nebula is Pn = 6.8 × 10-9 Pa, what is the average temperature (in K) of the nebula? Assume the mass of the sun is Ms = 1.989 × 1030 kg and the mass of a hydrogen atom is mH = 1.67 × 10-27 kg.
Physics
1 answer:
Oxana [17]3 years ago
8 0

Answer:

T=183.21K

Explanation:

We have to take into account that the system is a ideal gas. Hence, we have the expression

PV=nRT

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

V=\frac{4}{3}\pi r^3=\frac{4}{3}\pi (5.9*10^{15}m)^3=8.602*10^{47}m^3

V=8.86*10^{50}L

and for n

n=\frac{(4000M_s)/(2*mH)}{6.022*10^{23}mol^{-1}}=3.95*10^{36}mol

Hence, we have (1 Pa = 9.85*10^{-9}atm)

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

hope this helps!!

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