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Consider a classical gas of N indistinguishable non-interacting particles with ultra- relativistic energies, i.e. their kinetic energy - momentum relation is given by ɛ = pc, with c the speed of light and p the magnitude of the particle's momentum. The gas is confined to a box of volume V. (a) Compute the canonical partition function for this system. (b) Show that this system obeys the usual ideal gas law, pV = NkBT. (c) Show that the total average energy is, E = 3NKBT (and hence using (b) gives, E/V = 3p). (d) Show that the ratio of specific heats is, C,/Cv = 4/3. %3|

Consider a classical gas of N indistinguishable non-interacting particles with ultra- relativistic energies, i.e. their kinetic energy - momentum relation is given by ɛ = pc, with c the speed of light and p the magnitude of the particle's momentum. The gas is confined to a box of volume V. (a) Compute the canonical partition function for this system. (b) Show that this system obeys the usual ideal gas law, pV = NkBT. (c) Show that the total average energy is, E = 3NKBT (and hence using (b) gives, E/V = 3p). (d) Show that the ratio of specific heats is, C,/Cv = 4/3. %3|

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Consider a classical gas of N indistinguishable non-interacting particles with ultra- relativistic energies, i.e. their kinetic energy - momentum relation is given by ɛ = pc, with c the speed of light and p the magnitude of the particle's momentum. The gas is confined to a box of volume V. (a) Compute the canonical partition function for this system. (b) Show that this system obeys the usual ideal gas law, pV = NkBT. (c) Show that the total average energy is, E = 3NKBT (and hence using (b) gives, E/V = 3p). (d) Show that the ratio of specific heats is, C,/Cv = 4/3. %3|
Transcribed Image Text:Consider a classical gas of N indistinguishable non-interacting particles with ultra- relativistic energies, i.e. their kinetic energy - momentum relation is given by ɛ = pc, with c the speed of light and p the magnitude of the particle's momentum. The gas is confined to a box of volume V. (a) Compute the canonical partition function for this system. (b) Show that this system obeys the usual ideal gas law, pV = NkBT. (c) Show that the total average energy is, E = 3NKBT (and hence using (b) gives, E/V = 3p). (d) Show that the ratio of specific heats is, C,/Cv = 4/3. %3|
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