Thermodynamics- rms translational kinetic energy

AI Thread Summary
The discussion revolves around calculating the root mean square (rms) translational kinetic energy of 5 moles of helium gas in a 1m^3 container at 50°C, using the equation Total E = 3/2 nRT. A participant initially misapplied the equation, calculating the total energy as 20140.7 J, but realized the question specifically asks for energy per atom. The correct approach involves dividing the total energy by the number of atoms to find the energy per atom. The final correct answer for the rms translational kinetic energy is 6.7 x 10^-21 J. This highlights the importance of understanding the specific requirements of thermodynamics problems.
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Homework Statement


A container having a volume of 1m^3 holds 5 moles of helium gas at 50C. If the helium behaves like an ideal gas, the rms translational kinetic energy is?

Homework Equations


Total E= 3/2 nRT

The Attempt at a Solution


I tried solving this question using this equation, but I did not get the right answer.
The correct answer is 6.7 x 10^-21 J
 
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Please, show your work. ehild
 
Total Ek= 3/2 nRT
= 3/2 x 5 x 8.314 x 323
= 20140.7J, but this answer is wrong
 
The problem is asking for the energy per atom.
 
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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