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)