给学生讲解这一道题，主要是是用气体实验定律---**Text Extraction:**
13. 如图是某铸造原理示意图，往气室注入空气增加压强，使金属液沿升液管进入已预热的铸型室，待铸型室内金属液冷却凝固后获得铸件。柱状铸型室通过排气孔与大气相通，大气压强 p₀ = 1.0×10⁵ Pa，铸型室底面积 S₁ = 0.2m²，高度 h₁ = 0.2m，底面与注气前气室内金属液面高度差 H = 0.15m，柱状气室底面积 S₂ = 0.8m²，注气前气室内气体压强为 p₀，金属液的密度 ρ = 5.0×10³ kg/m³，重力加速度取 g = 10m/s²，空气可视为理想气体，不计升液管的体积。
(1) 求金属液刚好充满铸型室时，气室内金属液面下降的高度 h₂ 和气室内气体压强 p₁。
(2) 若在注气前关闭排气孔使铸型室密封，且注气过程中铸型型室内温度不变，求注气后铸型室内的金属液高度为 h₃ = 0.04m 时，气室内气体压强 p₂。
**Chart/Diagram Description:**
* **Type:** Schematic diagram illustrating a casting principle.
* **Main Elements:**
* **气室 (Gas Chamber):** A rectangular chamber at the bottom, containing 金属液 (Metal liquid). Labelled with base area S₂ (implied).
* **铸型室 (Mold Chamber):** A rectangular chamber positioned above the gas chamber. Labelled with base area S₁ and height h₁. Has a 排气孔 (Vent hole) at the top and a 进气阀 (Inlet valve) on the left side connected to the gas chamber.
* **升液管 (Rising Tube):** A vertical tube connecting the gas chamber (starting from the metal liquid level) to the bottom of the mold chamber.
* **排气孔 (Vent Hole):** Located on top of the mold chamber.
* **进气阀 (Inlet Valve):** Located on the side of the gas chamber, connected to something external (presumably for injecting air).
* **金属液 (Metal liquid):** The liquid filling the lower part of the gas chamber and rising into the rising tube and mold chamber.
* **Labels and Annotations:**
* 排气孔 (Vent Hole)
* 进气阀 (Inlet Valve)
* 铸型室 (Mold Chamber)
* 气室 (Gas Chamber)
* 升液管 (Rising Tube)
* 金属液 (Metal liquid)
* h₁: Vertical distance representing the height of the mold chamber.
* H: Vertical distance between the initial metal liquid level in the gas chamber and the bottom of the mold chamber.
* h₂: Vertical distance indicating the drop in the metal liquid level within the gas chamber from its initial position.
* **Relative Position and Direction:** The mold chamber is positioned directly above the gas chamber. The rising tube goes from the metal liquid in the gas chamber up into the bottom of the mold chamber. The inlet valve enters the gas chamber. The vent hole is on top of the mold chamber. Arrows indicate heights h₁, H, and h₂. The initial metal liquid level in the gas chamber is indicated by a dashed line.