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## Homework Statement

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?

## Homework Equations

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?

Thank you.