4. The partition function of asystem of indistinguishable particles is given by $Z=e^{aT^3V}$ where a is constant,T the tempwrature ,v the volume Calculate the pressure, internal energy, entropy, heat capacity
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Consider a system made up of $N$ particles. The energy per particle is given by $(E\rangle=\left(\Sigma F_{1} e^{-E_{1}} / k_{B} T\right) / Z,$ where $Z$ is the partition function defined in equation 36.29 . If this is a two-state system with $E_{1}=0$ and $E_{2}=E$ and $g_{1}=g_{2}=1,$ calculate the heat capacity of the system, defined as $N(d(E) / d T)$ and approximate its behavior at very high and very low temperatures (that is, $k_{\mathrm{R}} T \gg 1$ and $\left.k_{\mathrm{B}} T \propto 1\right)$.
Consider a system made up of $N$ particles. The average energy per particle is given by $\langle E\rangle=\left(\sum E_{i} e^{-E_{i} / k_{B} T}\right) / Z$ where $Z$ is the partition function defined in equation $36.29 .$ If this is a two-state system with $E_{1}=0$ and $E_{2}=E$ and $g_{1}=$ $g_{2}=1,$ calculate the heat capacity of the system, defined as $N(d\langle E\rangle / d T)$ and approximate its behavior at very high and very low temperatures (that is, $k_{\mathrm{B}} T \gg 1$ and $k_{\mathrm{B}} T \ll 1$ ).
A window receives 600 Btu/h of heat transfer at the inside surface of $70 \mathrm{F}$ and transmits the 600 Btu/h from its outside surface at $36 \mathrm{F}$, continuing to ambient air at $23 \mathrm{F}$. Find the flux of entropy at all three surfaces and the window's rate of entropy generation.
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