На пол действует сила тяжести шкафа F=m*g
А на шкаф действует сила реакции опоры (пола) N=m*g
3 В
2 А
1Б
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P1*g*h1=p2*g*h2
<span>h2=p1*h1/p2=1*13,6/13,6=1 см</span>
Имеем, что
![P_{1}=1.5*10^6 MPa, \ P_{2}=1.75*10^6 MPa, \ V_{1}=100 l=0.1 m^3, \ V_{2}=0.13 m^3, \ T=300 K, \ T=const.](https://tex.z-dn.net/?f=P_%7B1%7D%3D1.5%2A10%5E6+MPa%2C+%5C+P_%7B2%7D%3D1.75%2A10%5E6+MPa%2C+%5C+V_%7B1%7D%3D100+l%3D0.1+m%5E3%2C+%5C+V_%7B2%7D%3D0.13+m%5E3%2C+%5C+T%3D300+K%2C+%5C+T%3Dconst.)
Обозначим
![N_{1}](https://tex.z-dn.net/?f=N_%7B1%7D)
число частиц в первом баллоне,
![N_{2}](https://tex.z-dn.net/?f=N_%7B2%7D)
во втором и
![N](https://tex.z-dn.net/?f=N)
число частиц после соединения баллонов.
![P_{1}V_{1}=N_{1}kT \Rightarrow N_{1}=\frac{P_{1}V_{1}}{kT}\\ P_{2}V_{2}=N_{2}kT \Rightarrow N_{2}=\frac{P_{2}V_{2}}{kT}.](https://tex.z-dn.net/?f=P_%7B1%7DV_%7B1%7D%3DN_%7B1%7DkT+%5CRightarrow%C2%A0N_%7B1%7D%3D%5Cfrac%7BP_%7B1%7DV_%7B1%7D%7D%7BkT%7D%5C%5C+P_%7B2%7DV_%7B2%7D%3DN_%7B2%7DkT%C2%A0%5CRightarrow%C2%A0N_%7B2%7D%3D%5Cfrac%7BP_%7B2%7DV_%7B2%7D%7D%7BkT%7D.)
Поскольку после соединения баллонов
![N = N_{1}+N_{2}](https://tex.z-dn.net/?f=N+%3D+N_%7B1%7D%2BN_%7B2%7D)
, то
![PV=NkT \Rightarrow PV=(N_{1}+N_{2})kT \Rightarrow P=\frac{(N_{1}+N_{2})kT}{V} \Rightarrow P=\frac{\frac{(\frac{P_{1}V_{1}}{kT}+\frac{P_{2}V_{2}}{kT})}{kT}}{V_{1}+V_{2}}=\frac{P_{1}V_{1}+P_{2}V_{2}}{V_{1}+V_{2}}.](https://tex.z-dn.net/?f=PV%3DNkT+%5CRightarrow%C2%A0PV%3D%28N_%7B1%7D%2BN_%7B2%7D%29kT+%5CRightarrow+P%3D%5Cfrac%7B%28N_%7B1%7D%2BN_%7B2%7D%29kT%7D%7BV%7D%C2%A0%5CRightarrow%C2%A0%C2%A0P%3D%5Cfrac%7B%5Cfrac%7B%28%5Cfrac%7BP_%7B1%7DV_%7B1%7D%7D%7BkT%7D%2B%5Cfrac%7BP_%7B2%7DV_%7B2%7D%7D%7BkT%7D%29%7D%7BkT%7D%7D%7BV_%7B1%7D%2BV_%7B2%7D%7D%3D%5Cfrac%7BP_%7B1%7DV_%7B1%7D%2BP_%7B2%7DV_%7B2%7D%7D%7BV_%7B1%7D%2BV_%7B2%7D%7D.)
Подставим полученное выражение для P в уравнение Менделеева <span>- Клапейрона:
</span>
![PV=\frac{m}{M}RT, \ \rho = \frac{m}{V}=\frac{PM}{RT}=\frac{P_{1}V_{1}+P_{2}V_{2}}{V_{1}+V_{2}}*\frac{M}{RT}=\frac{1.5*10^6*0.1+1.75*10^*0.13}{0.23}*\frac{40*10^{-3}}{8.31*300} \approx \bold{27.36 kg/m^3}](https://tex.z-dn.net/?f=PV%3D%5Cfrac%7Bm%7D%7BM%7DRT%2C+%5C+%5Crho+%3D+%5Cfrac%7Bm%7D%7BV%7D%3D%5Cfrac%7BPM%7D%7BRT%7D%3D%5Cfrac%7BP_%7B1%7DV_%7B1%7D%2BP_%7B2%7DV_%7B2%7D%7D%7BV_%7B1%7D%2BV_%7B2%7D%7D%2A%5Cfrac%7BM%7D%7BRT%7D%3D%5Cfrac%7B1.5%2A10%5E6%2A0.1%2B1.75%2A10%5E%2A0.13%7D%7B0.23%7D%2A%5Cfrac%7B40%2A10%5E%7B-3%7D%7D%7B8.31%2A300%7D+%5Capprox+%5Cbold%7B27.36+kg%2Fm%5E3%7D)