1. 1 $a=n^{-1/3}$ | 0.20 |
|
1. 2 Численное значение $a=8.51\cdot 10^{-12}~\text{м}$ | 0.20 |
|
2. 1 $W_p=\cfrac{e^2}{4\pi\varepsilon_0 a}$ | 0.20 |
|
2. 2 $E_T=k_B T$ | 0.20 |
|
2. 3 $\Gamma=\cfrac{e^2}{4\pi\varepsilon_0ak_BT}$ | 0.20 |
|
2. 4 Численное значение $\Gamma=111$ | 0.20 |
|
3. 1 $R=a/2$ | 0.10 |
|
3. 2 $V=\cfrac{4}{3}\pi R^3$ | 0.10 |
|
3. 3 $\rho=-\cfrac{6}{\pi}ne$ | 0.20 |
|
3. 4 Численное значение $\rho=-4.95\cdot 10^{14}~\text{Кл/м}^3$ | 0.20 |
|
4. 1 $\oint_S \vec E\cdot d\vec S=\cfrac{Q}{\varepsilon_0}$ | 0.20 |
|
4. 2 $\oint_S \vec E\cdot d\vec S=4\pi r^2E$ | 0.20 |
|
4. 3 $Q=e+\rho\cfrac{4}{3}\pi r^3$ | 0.20 |
|
4. 4 $E=\cfrac{e}{4 \pi \varepsilon_{0} r^{2}}+\cfrac{\rho r}{3 \varepsilon_{0}}$ | 0.20 |
|
4. 5 $\varphi(a / 4)-\varphi(a / 2)=-\int_{a / 2}^{a / 4} E d r$ | 0.20 |
|
4. 6 $\varphi(a / 4)-\varphi(a / 2)=\cfrac{5e}{16\pi\varepsilon_0 a}$ | 0.20 |
|
4. 7 $\varphi(a / 4)-\varphi(a / 2)=211~\text{В}$ | 0.20 |
|
5. 1 $m \ddot{r}=\cfrac{e \rho}{3 \varepsilon_{0}} r$ | 0.20 |
|
5. 2 $\omega_{p}=\sqrt{\cfrac{2 n e^{2}}{\pi m_{p} \varepsilon_{0}}}$ | 0.20 |
|
5. 3 Численное значение $\omega_p=2.94\cdot 10^{16}~\text{с}^{-1}$ | 0.20 |
|
6. 1 $v=\sqrt{\cfrac{k_{B} T}{m_{p}}}$ | 0.20 |
|
6. 2 $A=\cfrac{\nu}{\omega_p}$ | 0.20 |
|
6. 3 Численное значение $A=2.85\cdot 10^{-13}~\text{м}$ | 0.20 |
|
7. 1 $dq=4\pi r^2\rho dr$ | 0.20 |
|
7. 2 $W_1=-\cfrac{3e^2}{4\pi\varepsilon_0 a}$ | 0.20 |
|
7. 3 $w=\cfrac{1}{2}\varepsilon_0 E^2$ | 0.20 |
|
7. 4 $W_2=\cfrac{3e^2}{10\pi\varepsilon_0 a}$ | 0.20 |
|
7. 5 $W=-\cfrac{9e^2}{20\pi\varepsilon_0 a}$ | 0.20 |
|
7. 6 $E=3Nk_B T$ | 0.20 |
|
7. 7 $U=E+N W=3 N k_{B} T-\cfrac{9 e^{2}}{20 \pi \varepsilon_{0}} \cfrac{N^{4 / 3}}{V^{1 / 3}}$ | 0.20 |
|
7. 8 $\alpha_1=3k_B T$ | 0.20 |
|
7. 9 $\alpha_2=-\cfrac{9e^2}{20\pi\varepsilon_0}$ | 0.20 |
|
8. 1 $W=-\cfrac{9 e^{2} n^{1 / 3}}{20 \pi \varepsilon_{0}}$ | 0.20 |
|
8. 2 $V'=2V$ | 0.20 |
|
8. 3 $e'=2e$ | 0.20 |
|
8. 4 $W^{\prime}=-2^{5 / 3} \cfrac{9 e^{2} n^{1 / 3}}{20 \pi \varepsilon_{0}}$ | 0.20 |
|
8. 5 $\delta U_{c}=\cfrac{\left(2^{2 / 3}-1\right) 9 e^{2} n^{1 / 3}}{10 \pi \varepsilon_{0}}$ | 0.20 |
|
8. 6 Численное значение $\delta U_c=5.72\cdot 10^{-17}~\text{Дж}$ | 0.20 |
|
9. 1 $A=\left(\cfrac{\partial P}{\partial T}\right)_{V}\left(T_{A B}-T_{C D}\right)\left(V_{B}-V_{A}\right)$ | 0.20 |
|
9. 2 $U_{B}-U_{A}=\left(\cfrac{\partial U}{\partial V}\right)_{T}\left(V_{B}-V_{A}\right)$ | 0.20 |
|
9. 3 $Q=U_B-U_A+P(V_B-V_A)$ | 0.20 |
|
9. 4 $\cfrac{A}{Q}=\cfrac{T_{AB}-T_{CD}}{T_{AB}}$ | 0.20 |
|
9. 5 $\left(\cfrac{\partial U}{\partial V}\right)_{T}=T\left(\cfrac{\partial P}{\partial T}\right)_{V}-P$ | 0.20 |
|
10. 1 $T\left(\cfrac{\partial P}{\partial T}\right)_{V}-P=\cfrac{3 e^{2}}{20 \pi \varepsilon_{0}} \cfrac{N^{4 / 3}}{V^{4 / 3}}$ | 0.20 |
|
10. 2 $P(T, V)=C(V) T-\cfrac{3 e^{2}}{20 \pi \varepsilon_{0}} \cfrac{N^{4 / 3}}{V^{4 / 3}}$ | 0.20 |
|
10. 3 $\left.P(T, V)\right|_{e \rightarrow 0}=\cfrac{N k_{B} T}{V}$ | 0.20 |
|
10. 4 $P(T, V)=\cfrac{N k_{B} T}{V}-\cfrac{3 e^{2}}{20 \pi \varepsilon_{0}} \cfrac{N^{4 / 3}}{V^{4 / 3}}$ | 0.20 |
|
10. 5 $\beta_1=k_BT$ | 0.20 |
|
10. 6 $\beta_2=-\cfrac{3e^2}{20\pi\varepsilon_0}$ | 0.20 |
|
10. 7 $\beta_3=\cfrac{4}{3}$ | 0.20 |
|
10. 8 Численный ответ $P=-2.59\cdot 10^{16}~\text{Па}$ | 0.20 |
|