Respuesta :
1) Average velocity of the H2 molecules is zero
2) Average energy at 300 K: [tex]1.04\cdot 10^{-20} J[/tex], at 6000 K: [tex]2.07\cdot 10^{-19} J[/tex]
3) Rms velocity at 300 K: 2497 m/s, at 6000 K: 11,167 m/s
4) Time taken for molecules at 300 K: [tex]6.01\cdot 10^7 s[/tex] , for molecules at 6000 K: [tex]1.34\cdot 10^7 s[/tex]
Explanation:
1)
The average velocity of the particles in a gas is always zero.
In fact, the average velocity is given by the vector sum of all the velocities of the individual particles, divided by the number of particles (N):
[tex]v_{avg} = \frac{v_1+v_2+v_3+...+v_N}{N}[/tex]
However, the particles in a gas have random motion, according to the kinetic theory: therefore, since a gas contains a huge number of molecules, there are always two particles having velocity in a direction opposite to each other, and therefore, the average velocity of the molecules is zero.
2)
The average energy of the particles in a biatomic gas, such as the [tex]H_2[/tex] in this problem, is given by the equation
[tex]E=\frac{5}{2}kT[/tex] (1)
where
[tex]k=1.38\cdot 10^{-23} J/K[/tex] is the Boltzmann's constant
T is the Kelvin temperature in the gas
For the hydrogen gas in the room,
T = 300 K
Therefore the average energy is
[tex]E=\frac{5}{2}(1.38\cdot 10^{-23})(300)=1.04\cdot 10^{-20} J[/tex]
For solar photosphere instead,
T = 6000 K
So the average energy is
[tex]E=\frac{5}{2}(1.38\cdot 10^{-23})(6000)=2.07\cdot 10^{-19} J[/tex]
3)
The average kinetic energy of the particles in a gas can be written as:
[tex]E=\frac{1}{2}mv^2[/tex]
where
m is the mass of one particle
v is the rms velocity
We can equate this equation to eq.(1) written in part 2):
[tex]\frac{1}{2}mv^2=\frac{5}{2}kT[/tex]
And re-arranging, we find an expression for the rms speed:
[tex]v=\sqrt{\frac{5kT}{m}}[/tex]
The mass of a molecules of hydrogen is twice the mass of a proton,
[tex]m=3.32\cdot 10^{-27}kg[/tex]
And therefore, the rms speed at room temperature (T=300 K) is
[tex]v=\sqrt{\frac{5(1.38\cdot 10^{-23})(300)}{3.32\cdot 10^{-27}}}=2497 m/s[/tex]
While for the solar photosphere (T=6000 K) the rms speed is
[tex]v=\sqrt{\frac{5(1.38\cdot 10^{-23})(6000)}{3.32\cdot 10^{-27}}}=11,167 m/s[/tex]
4)
The distance between Earth and the Sun is (on average)
[tex]d=1.50\cdot 10^8 km = 1.50\cdot 10^{11} m[/tex]
The motion of the molecules can be assumed to be a uniform motion, so we can use the equation
[tex]d=vt[/tex]
where
d is the distance covered
v is the rms velocity of the molecules
t is the time taken
Therefore, for the molecules at T = 300 K the time taken would be:
[tex]t=\frac{d}{v}=\frac{1.50\cdot 10^{11}}{2497}=6.01\cdot 10^7 s[/tex]
While for the molecules of the photosphere (T=6000 K) the time taken is
[tex]t=\frac{d}{v}=\frac{1.50\cdot 10^{11}}{11,167}=1.34\cdot 10^7 s[/tex]
Learn more about ideal gases:
brainly.com/question/9321544
brainly.com/question/7316997
brainly.com/question/3658563
About average velocity:
brainly.com/question/8893949
brainly.com/question/5063905
About kinetic energy:
brainly.com/question/6536722
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