At low temperature the specific heat of hydrogen is due to
Answers
Explanation:
At normal temperatures and pressures hydrogen is found as a diatomic molecule.
As a diatomic molecule it can store kinetic energy in three translational degrees of freedom, x,y and z axes and in two rotational modes about two axes. The third rotational mode cannot store energy as it is about a symmetrical axis. Simple harmonic motion of the molecule is generally locked out of equipartition at these temperatures as the energy required is too high to be compatible with the energy distribution of the other modes. At very high temperatures these additional heat storage modes do add to the gases heat capacity.
For each degree of freedom we can assign 1/2kT=1/2mv(mean)^2, such that each molecule can store 5/2kT of energy having 5degree of freedom.
We can scale this to molar capacities by replacing k with R such that the molar heat capacity becomes 5/2RT
We can then calculate the isochoric specific heat capacity by dividing by the molecular mass of the hydrogen molecule, given R=8.31 J/mol.K and molar mass of dhydrogen is 2.016g/mol.
This gives Cv = 10.31 J/kg.K which represents the specific heat capacity of hydrogen at constant volume (gas in a container).
Likewisewe can calculate the isobaric specific heat capacity using Cp = Cv +R
hence we now have energy storage as 7/2RT per mole which gives our isobaric specific heat capacity as,
Cp = 14.4 J/kg.K which allows for thermodynamic work as the gas changes volume in a pressurised environment, from first principles.
Answer:
Explanation:
At normal temperatures and pressures hydrogen is found as a diatomic molecule.
As a diatomic molecule it can store kinetic energy in three translational degrees of freedom, x,y and z axes and in two rotational modes about two axes. The third rotational mode cannot store energy as it is about a symmetrical axis. Simple harmonic motion of the molecule is generally locked out of equipartition at these temperatures as the energy required is too high to be compatible with the energy distribution of the other modes. At very high temperatures these additional heat storage modes do add to the gases heat capacity.
For each degree of freedom we can assign 1/2kT=1/2mv(mean)^2, such that each molecule can store 5/2kT of energy having 5degree of freedom.
We can scale this to molar capacities by replacing k with R such that the molar heat capacity becomes 5/2RT
We can then calculate the isochoric specific heat capacity by dividing by the molecular mass of the hydrogen molecule, given R=8.31 J/mol.K and molar mass of dhydrogen is 2.016g/mol.
This gives Cv = 10.31 J/kg.K which represents the specific heat capacity of hydrogen at constant volume (gas in a container).
Likewisewe can calculate the isobaric specific heat capacity using Cp = Cv +R
hence we now have energy storage as 7/2RT per mole which gives our isobaric specific heat capacity as,
Cp = 14.4 J/kg.K which allows for thermodynamic work as the gas changes volume in a pressurised environment, from first principles.