Question

The rms speed of the molecules in 2.0 g of hydrogen gas is 1800 m/s.

What is the total translational kinetic energy of the gas molecules? ________kJ
Answer not 1.62kJ

What is the thermal energy of the gas? __5.4kJ___ <----That is the right answer.

500 J of work are done to compress the gas while, in the same process, 1400 J of heat energy are transferred from the gas to the environment. Afterward, what is the rms speed of the molecules? ____________m/s
Answer not 1549 m/s

Answer 1

rms speed v = 1800 m/s, mass m = 2.0 g, mole mass M = 2.0g/mol, mole number n = m/M = 1.0
a) the total translational kinetic energyof the gas molecules
E_t = mv²/2 = 2.0*10^-3 *1800²/2 = 3240 J = 3nRT/(2M)
b) the thermal energy of thegas
E = 5nRT/(2M) = (5/3) *[3nRT/(2M)] = (5/3)*E_t =5400 J = 5.4 kJ
c) Q = 1400 J, W = 500 J, final temperature = T', thermal energy =E', rms speed = v'
ΔE = W - Q = -900 J = E' - E
so E' = E + ΔE = 4500 J
E' = 5nRT'/(2M) = (5/3)*E_t' = (5/3)mv'²/2
v' = √(6E'/5m) = 1643 m/s