How Is Deuteron Kinetic Energy Related to Plasma Temperature in Nuclear Fusion?

AI Thread Summary
The discussion focuses on the relationship between deuteron kinetic energy and plasma temperature in nuclear fusion. The user is trying to calculate the root mean square (rms) speed of deuterons and the corresponding plasma temperature, using the formula Vrms = √(3KT/m). The user expresses frustration over not obtaining the expected temperature of 5.9x10^10 K, despite using the correct constants for Boltzmann's constant and the mass of the deuteron. Another participant points out that the provided rms speed of 9.0×10−2 m/s is unrealistic, as typical rms speeds for deuterons at room temperature are around 2000 m/s. The conversation emphasizes the importance of accurate values in calculations related to nuclear fusion.
jensgt
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Homework Statement


A deuteron, , is the nucleus of a hydrogen isotope and consists of one proton and one neutron. The plasma of deuterons in a nuclear fusion reactor must be heated to about 3.01×108 . What is the rms speed of the deuterons?

What would the temperature of the plasma be if the deuterons had an rms speed equal to 9.0×10−2 ?


Homework Equations



Vrms = √(3KT/m)

1/2mv2 = 3/2KT

mVrms2/(3K) = T


The Attempt at a Solution



I went over this about 100 times before giving up. The answer I know is 5.9x1010K but even with that I can't get the answer. It is driving me sort of crazy so I figured I would ask if someone could help. The K I am using is 1.38x10-23J/K and the m is 3.34x10-27kg

help!
 
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Use units, please. In what unit the rms speed has to be 9.0×10−2 and temperature 3.01×108?

ehild
 
Speed = m/s and temp = K
 
Have you copied the rms speed correctly? 9.0x10-2 m/s is unrealistic. Even at room temperature, the rms speed is about 2000 m/s for the deuteron.

ehild
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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