IB Science: Energy Key Concepts | IB 科学：能量考点精讲

📚 IB Science: Energy Key Concepts | IB 科学：能量考点精讲

Energy is one of the most fundamental concepts in IB science, bridging physics, chemistry, and biology. A solid grasp of work, energy conservation, power, and efficiency is essential for tackling mechanics problems and understanding systems at all scales. This revision guide distils the key energy principles, common pitfalls, and exam strategies you need for success.

能量是 IB 科学中最基本的概念之一，贯穿物理、化学和生物各个学科。扎实掌握功、能量守恒、功率和效率，对于解决力学问题以及理解各尺度下的系统至关重要。这份考点精讲提炼了核心能量原理、常见错误和考试策略，助你从容应对。

1. Defining Energy | 能量的定义

Energy is the capacity to do work. It is a scalar quantity, having magnitude but no direction. The SI unit of energy is the joule (J), where 1 J is the work done when a force of 1 newton moves an object through 1 metre.

能量是做功的能力。它是一个标量，只有大小没有方向。能量的国际单位是焦耳 (J)，1 J 即 1 牛顿的力使物体移动 1 米所做的功。

Energy exists in many forms: kinetic, gravitational potential, elastic potential, chemical, thermal (internal), nuclear, and electromagnetic. All forms can be transformed from one to another, while the total energy in an isolated system remains constant.

能量存在多种形式：动能、重力势能、弹性势能、化学能、热能（内能）、核能及电磁能。在孤立系统中，所有形式的能量都可以相互转化，但总能量保持不变。

2. Work and Energy Transfer | 功与能量转移

Work (W) is a mechanical transfer of energy caused by a force acting over a displacement. When a constant force F moves an object a distance s with an angle θ between the force and displacement vectors, the work done is:

功 (W) 是力作用于物体使其发生位移时引起的机械能转移。当恒力 F 移动物体距离 s，且力与位移之间的夹角为 θ 时，做功为：

W = F s cos θ

If the force is parallel to displacement (θ = 0°), W = F s. If the force is perpendicular (θ = 90°), no work is done. Positive work adds energy to the system; negative work removes energy from it.

若力与位移平行（θ = 0°），则 W = F s。若力与位移垂直（θ = 90°），则不做功。正功使系统获得能量，负功使系统损失能量。

The area under a force–displacement graph represents the work done. For a varying force, this graphical interpretation is often used in IB questions, rather than calculus.

力-位移图下的面积表示所做的功。对于变力，IB 常使用图像法而非积分来进行分析。

3. Kinetic Energy | 动能

Kinetic energy (Eₖ) is the energy an object possesses due to its motion. It is given by:

动能 (Eₖ) 是物体由于运动而具有的能量，其表达式为：

Eₖ = ½ m v²

This equation shows that doubling the speed quadruples the kinetic energy, while doubling the mass only doubles it. The work–energy theorem states that the net work done on an object equals its change in kinetic energy: W_net = ΔEₖ.

该公式表明，速度加倍会使动能增至四倍，而质量加倍仅使动能翻倍。功能定理指出，物体所受的净功等于其动能的改变量：W_net = ΔEₖ。

Kinetic energy is always non-negative and depends on the reference frame. Always make sure you use the same frame for initial and final energies in a problem.

动能恒为非负值，且与参考系有关。解题时务必对初末状态使用同一参考系进行计算。

4. Gravitational Potential Energy | 重力势能

Gravitational potential energy (Eₚ) is energy stored due to an object’s position in a gravitational field. Near the Earth’s surface, where the field can be considered uniform, it is:

重力势能 (Eₚ) 是物体在重力场中因位置而储存的能量。在地球表面附近，重力场可视为匀强场，表达式为：

Eₚ = m g h

Here h is the vertical height above an arbitrary reference level. Only changes in potential energy are physically meaningful; the choice of zero point does not affect energy differences.

其中 h 是所选参考水平面以上的垂直高度。物理上只有势能的变化才有意义；零势能点的选取不影响势能差。

Strictly, this formula is valid only when g is constant. For large altitude changes, the more general expression −G M m / r must be used, but in most IB problems the uniform approximation holds.

严格来说，该公式仅在 g 不变时成立。若高度变化很大，需使用通用表达式 −G M m / r，但在大多数 IB 题目中匀强场近似已足够。

5. Elastic Potential Energy | 弹性势能

When a spring or other elastic object is deformed, elastic potential energy is stored. For an ideal spring obeying Hooke’s law (F = k x, where k is the spring constant), the energy stored is:

弹簧或其他弹性物体发生形变时会储存弹性势能。对于满足胡克定律（F = k x，k 为劲度系数）的理想弹簧，储存的能量为：

Eₑ = ½ k x²

x is the extension or compression from the spring’s natural length. The same formula applies whether the spring is stretched or compressed. The area under the force–extension graph equals Eₑ.

x 是相对于弹簧原长的伸长量或压缩量。无论弹簧被拉伸还是压缩，公式均相同。力-伸长量图下的面积即为 Eₑ。

6. Conservation of Energy | 能量守恒

The principle of conservation of energy states that energy cannot be created or destroyed; it can only be transferred or transformed from one form into another. In an isolated system, the total energy remains constant.

能量守恒定律指出，能量既不能被创造也不能被消灭，只能从一种形式转化为另一种形式，或从一个物体转移给另一个物体。在孤立系统中，总能量保持不变。

A classic example: a falling object converts Eₚ into Eₖ. If air resistance is negligible, mechanical energy is conserved. When friction is present, some mechanical energy is dissipated as thermal energy, but total energy is still conserved.

经典例子：下落物体将重力势能转化为动能。若空气阻力可忽略，则机械能守恒。当存在摩擦时，部分机械能耗散为热能，但总能量依然守恒。

In IB exams, you will often combine the conservation of energy with the work–energy theorem to solve problems involving inclined planes, pendulums, or collisions where resistive forces act.

在 IB 考试中，你常需要结合能量守恒与功能定理来求解涉及斜面、单摆或存在阻力的碰撞问题。

7. Power | 功率

Power (P) is the rate of doing work or transferring energy. The SI unit is the watt (W), where 1 W equals 1 J s⁻¹. Average power is:

功率 (P) 是做功或转移能量的速率。国际单位是瓦特 (W)，1 W 等于 1 J s⁻¹。平均功率为：

P = W / t = ΔE / t

When a constant force F acts on an object moving at constant speed v in the direction of the force, the instantaneous power is given by:

当恒力 F 作用在沿力方向以恒速度 v 运动的物体上时，瞬时功率为：

P = F v

This relation is particularly useful for problems involving vehicles, lifting machinery, or any system where force and velocity are known.

这一关系在涉及交通工具、提升机械或已知力与速度的任何系统中尤其有用。

8. Efficiency | 效率

Efficiency (η) indicates how well a system converts input energy into useful output. It is expressed as a ratio, often quoted as a percentage:

效率 (η) 表示系统将输入能量转化为有用输出的程度，通常以百分比表示：

η = (useful energy output / total energy input) × 100%

In power terms, the same formula becomes η = (useful power output / total power input) × 100%. Real processes always have η < 100% because some energy is inevitably dissipated as heat, sound, or vibration.

在功率表述下，公式变为 η = (有用输出功率 / 总输入功率) × 100%。实际过程的效率总是低于 100%，因为总有一部分能量不可避免地耗散为热、声或振动。

9. Sankey Diagrams and Energy Transformations | 桑基图与能量转化

A Sankey diagram uses arrows whose widths are proportional to the amount of energy being transferred. Input energy is shown on the left, branching into useful output and wasted energy on the right.

桑基图使用宽度与传递能量成正比的箭头，左侧为输入能量，右侧分支为有用输出和浪费的能量。

When drawing or interpreting a Sankey diagram, clearly label each energy form (e.g., electrical, light, heat). The total width of the output arrows must equal the width of the input arrow. IB questions may ask you to calculate efficiency from such a diagram.

绘制或解读桑基图时，要明确标出每种能量形式（如电能、光能、热能）。输出端箭头的总宽度必须等于输入端箭头的宽度。IB 考试可能会要求根据桑基图计算效率。

10. Exam Tips and Common Pitfalls | 考试技巧与常见错误

Always identify the system you are analysing and check whether external forces do work. If several forces act, compute the net work to find the change in kinetic energy.

始终明确你分析的系统，并检查外力是否做功。若有多个力作用，计算净功以求动能变化。

Pay careful attention to units: convert km/h to m/s, grams to kilograms, and ensure consistent SI units throughout. Do not confuse power (rate) with energy (quantity).

仔细处理单位：将 km/h 转换为 m/s，克转换为千克，并全程使用统一的国际单位。切勿混淆功率（速率）与能量（总量）。

A common mistake is applying Eₚ = m g h in non-uniform fields or forgetting that the work done by gravity depends only on vertical height difference, not on the path taken.

一个常见错误是在非匀强场中使用 Eₚ = m g h，或忘记重力做的功只取决于竖直高度差，与路径无关。

When using conservation of energy, take care to include all forms of energy present. If thermal effects are important, they must be accounted for, even if only as an unknown energy loss.

运用能量守恒时，注意包含所有存在的能量形式。如果热效应很重要，即使只是未知的能量损失，也必须将其纳入考量。

Practise sketching and interpreting force–displacement and force–extension graphs to find work or elastic energy. Be ready to combine kinetic, potential, and spring energies with work–energy principles to find speeds, heights, or maximum compressions.

多加练习力-位移图和力-伸长量图的绘制与解读，以求出功或弹性势能。做好将动能、势能和弹簧能量与功能原理结合，求解速度、高度或最大压缩量的准备。

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IB Science: Energy Key Concepts | IB 科学：能量 考点精讲