What is the Most Probable Speed of a Gas at a Given Temperature?

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To determine the most probable speed of a gas at a given temperature, the relevant equation involves the use of kinetic energy and the ideal gas constant. The average kinetic energy can be calculated using the formula \(\sqrt{kRT}\), where R is the ideal gas constant and T is the temperature. The probability distribution of gas particle speeds is given by the equation \(v^2 e^{-m v^2/{2 k_B T}}\). To find the most probable speed, one must set the derivative of this probability distribution to zero. Understanding these equations allows for the calculation of the most probable speed for gases like Argon at specific temperatures.
Romperstomper
I'm having problems trying to figure out the most probable speed of a gas with the only givens being what gas it is and the temperature of the gas, for example, find the most probable speed of Ar at 127C. The equation is Ke = 1/2mv^2.

I know how to get the average kinetic energy, speed, and total kinetic energy. But, I'm stuck on how to get the most probable speed or energy with just these two pieces of information.
 
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I believe the equation for the average kinetic energy of a gas is \sqrt{kRT}
Where R is the ideal gas constant, T is temperature and k is Boltzman's constant.
 
The probability of finding atoms with speeds between v and v + dv is proportional to v^2 e^{-m v^2/{2 k_B T}} and you can find the most probable speed by setting its derivative to 0.
 
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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