The atmosphere of the sun consists mostly of hydrogen atoms (not molecules) at a temperature of . What are (a) the average translational kinetic energy per atom and (b) the rms speed of the atoms?
(a) The average translational kinetic energy per atom is
(b) The rmsspeed of atom is
(a) The average translational kinetic energy of a molecule with mass m and velocity v is The average translational kinetic energy of a molecule is affected by its temperature, hence it is related to the temperature t per molecule in the manner
Where is Boltzmann's constant and in unit its value is
Plug the values for and into equation (1) to get the energy for the atom
(b)The transitional energy depends on the temperature only not the mass of the gas. The molecule with mass and velocity has an average translational kinetic energy and it is given by equation in the form
As shown, both equations have the same left side, so we can use these expressions to get an equation for root mean square velocity
The mass of the hydrogen atom is the same for one proton . Now, we plug the values for and into equation (3) to get
moles of a diatomic gas with has initial pressure and volume . The gas undergoes a process in which the pressure is directly proportional to the volume until the speed of the molecules has doubled.
a. Show this process on a diagram.
b. How much heat does this process require? Give your answer in terms of , , and .
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