So this is the final section of a problem I had posted earlier, and I'm kinda stumped again.
The rms speed of the molecules in 1.2 g of hydrogen gas is 1800 m/s.
300 J of work are done to compress the gas while, in the same process, 1500 J of heat energy are transferred from the gas to the environment. Afterward, what is the rms speed of the molecules?
E = N(1/2)mc^2
m = Mass of H molecule = 1.67 x 10^-27 kg
N = Total # of Molecules = 7.19 x 10^23 Molecules
c = RMS speed
E(total) = E1 (initial energy) + E2 (300J of work) + E3 (1500 J lost to environment)
The Attempt at a Solution
initial Energy = N x (1/2)mC2
Which equates to 1.9 KJ earlier in the assignment.
E = (1900J) + (300J - the work done on the gas) - (1500J subtracted because it is lost to the environment)
= 700 J
Now plug this back in to solve for C^2
700J = N x (1/2)mc^2
700J = (7.19 x 10^23 Molecules)(1/2)(1.67 x 10^-27 kg)(C^2)
(c^2) = 1,166,083.6
c = 1,825 m/s
It is telling me I am wrong, so can someone shed some light on my mistake?