The rms speed of the molecules in 1.3 g of hydrogen gas is 1600 m/s. Part A. What is the total translational kinetic energy of the gas molecules?
Part B. What is the thermal energy of the gas?
Part C. 500J of work are done to compress the gas while, in the same process, 2000J of heat energy are transferred from the gas to the environment. Afterward, what is the rms speed of the molecules?

Explanation:

1.3  g = 1.3 / 2 = .65 moles of hydrogen .

.65 moles = 6.02 x 10²³  x .65 molecules

Translational kinetic energy of one molecule = 1/2 mc² where c is rms speed = 1/2 x 2 x 1.67 x 10⁻²⁷ x ( 1600 )² = 42752 x 10⁻²⁵ J

Translational kinetic energy of .65  moles = 6.02 x 10²³  x .65 x 42752 x 10⁻²⁵ J

= 1673 J  approx .

B )  Total thermal energy and total translational kinetic energy are same so

Thermal energy of gas = 1673 J

C )  Net content of thermal energy = 1673 + 500 - 2000 = 173 J  

If c be the rms speed

  1/2 x 2 x 1.67 x 10⁻²⁷ x .65 x  6.02 x 10²³ c² =  173

6.534 x 10⁻⁴ c² = 173

c² = 264769

c = 514.56 m /s

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