请帮我分析、讲解这道题---**Textual Information:**
**Problem Stem:**
14. 如图所示, 质量M = 4kg的圆柱形汽缸固定在倾角 $\theta = 30^{\circ}$ 的光滑斜面上, 一定量的空气(视为理想气体)被质量 $m_1 = 2kg$ 的活塞封闭在其中. 开始时活塞内表面相对汽缸底部的长度 $L_1 = 15cm$, 外界热力学温度 $T_0 = 300K$. 现用跨过定滑轮的轻绳将质量 $m_2 = 1.5kg$ 的重锤与活塞连接, 重新平衡后, 活塞沿斜面向上运动的位移 $x = 5cm$. 大气压强恒为 $p_0 = 1.0 \times 10^5 Pa$, 取重力加速度大小 $g = 10m/s^2$, 与活塞连接的轻绳始终平行于斜面, 汽缸壁导热良好, 活塞可沿汽缸壁无摩擦地滑动.
**Sub-questions:**
(1) 求活塞的横截面积;
(2) 若外界的温度缓慢降低 $\Delta T = 15K$, 为了使降温后活塞回到初始时的位置, 需要从汽缸底部的抽气阀门处抽出适量气体, 求抽出气体的质量与抽气前缸内气体质量的比值;
(3) 假设斜面和绳均足够长, 释放汽缸, 经过一段时间后活塞与汽缸相对静止, 求此时活塞内表面到汽缸底部的距离(此时重锤未到达定滑轮处, 结果以厘米为单位且保留一位小数).
**Given Parameters and Constants:**
* Cylinder mass: $M = 4kg$
* Inclination angle of the inclined plane: $\theta = 30^{\circ}$
* Piston mass: $m_1 = 2kg$
* Initial length of air column (piston inner surface to cylinder bottom): $L_1 = 15cm = 0.15m$
* Initial external thermodynamic temperature: $T_0 = 300K$
* Mass of suspended weight: $m_2 = 1.5kg$
* Displacement of piston upwards along the incline after connecting the weight: $x = 5cm = 0.05m$
* Atmospheric pressure: $p_0 = 1.0 \times 10^5 Pa$
* Acceleration due to gravity: $g = 10m/s^2$
* Rope connected to piston is parallel to the inclined plane.
* Cylinder wall is a good conductor of heat.
* Piston slides without friction along the cylinder wall.
* Air is considered an ideal gas.
**Supplementary Information:**
* For sub-question (3), the result should be in centimeters and rounded to one decimal place.
* For sub-question (3), assume the suspended weight has not reached the pulley.
**Chart/Diagram Description:**
* **Type:** Schematic diagram illustrating a physics setup.
* **Main Elements:**
* **Inclined Plane:** A surface tilted upwards from the horizontal, representing a slope.
* **Angle:** Labeled as $\theta$, indicating the angle of inclination of the plane with the horizontal.
* **Cylinder:** A cylindrical object resting on the inclined plane, oriented with its axis parallel to the slope. It appears to be fixed in place.
* **Piston:** A movable disc inside the cylinder, sealing a volume of gas within.
* **String/Rope:** A line extending from the piston, going upwards along the inclined plane, passing over a pulley.
* **Pulley:** A wheel mounted at the top/end of a vertical support structure. The string passes over it.
* **Suspended Weight:** An object hanging vertically from the string after it passes over the pulley.
* **Support Structure:** A vertical structure holding the pulley above the inclined plane.
* **Relative Position and Direction:** The cylinder is fixed on the inclined plane. The piston is inside the cylinder. The string is attached to the piston, runs parallel to the inclined plane, over the pulley, and down to the suspended weight. The suspended weight hangs below the pulley. The angle $\theta$ is shown between the inclined plane and the horizontal base.