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4. At very high temperatures (like in early Universe) the gas molecules move with very high speeds (comparable to the speed of light), and therefore, one has to take relativis- tic effects into account. In this case the relation between energy and momentum is no longer the non-relativistic expression E = p²/2m, but it has to be replaced with the rel- ativistic relation E = |p|c, where c is the speed of light and |p| = /p; + p3+ p?. Repeat the same steps we carried out in the class to derive the partition function of a non- relativistic ideal gas and show that the partition function for a single molecule in the relativistic gas is given by V K³T³ . c3 8л (0.4)

4. At very high temperatures (like in early Universe) the gas molecules move with very high speeds (comparable to the speed of light), and therefore, one has to take relativis- tic effects into account. In this case the relation between energy and momentum is no longer the non-relativistic expression E = p²/2m, but it has to be replaced with the rel- ativistic relation E = |p|c, where c is the speed of light and |p| = /p; + p3+ p?. Repeat the same steps we carried out in the class to derive the partition function of a non- relativistic ideal gas and show that the partition function for a single molecule in the relativistic gas is given by V K³T³ . c3 8л (0.4)

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Parts 1,2 and 3 have been answers in a previous so 3-6 is what I need to be solved. 

4. At very high temperatures (like in early Universe) the gas molecules move with very high speeds (comparable to the speed of light), and therefore, one has to take relativis- tic effects into account. In this case the relation between energy and momentum is no longer the non-relativistic expression E = p²/2m, but it has to be replaced with the rel- ativistic relation E = |p|c, where c is the speed of light and |p| = /p; + p3+ p?. Repeat the same steps we carried out in the class to derive the partition function of a non- relativistic ideal gas and show that the partition function for a single molecule in the relativistic gas is given by V K³T³ . c3 8л (0.4)
Transcribed Image Text:4. At very high temperatures (like in early Universe) the gas molecules move with very high speeds (comparable to the speed of light), and therefore, one has to take relativis- tic effects into account. In this case the relation between energy and momentum is no longer the non-relativistic expression E = p²/2m, but it has to be replaced with the rel- ativistic relation E = |p|c, where c is the speed of light and |p| = /p; + p3+ p?. Repeat the same steps we carried out in the class to derive the partition function of a non- relativistic ideal gas and show that the partition function for a single molecule in the relativistic gas is given by V K³T³ . c3 8л (0.4)
5. As we showed in the class, the total partition function of N molecules reads ZN hN N! (0.5) %D Use Z, and Equation (0.4) to find the pressure of the relativistic gas, P, as a function of V, N, T. 6. Find the total thermal energy of the relativistic gas U. Show that the relation between the pressure, total thermal energy and Volume for a relativistic gas is given by
Transcribed Image Text:5. As we showed in the class, the total partition function of N molecules reads ZN hN N! (0.5) %D Use Z, and Equation (0.4) to find the pressure of the relativistic gas, P, as a function of V, N, T. 6. Find the total thermal energy of the relativistic gas U. Show that the relation between the pressure, total thermal energy and Volume for a relativistic gas is given by
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