The First Law of Thermodynamics · 热力学第一定律
| English | 中文 | Pinyin · 拼音 |
|---|---|---|
| first law of thermodynamics/fɜːst lɔː ɒv ˌθɜːməʊdaɪˈnæmɪks/ | 热力学第一定律 | rè lì xué dì yí dìng lǜ |
| internal energy/ɪnˈtɜːnl ˈenədʒi/ | 内能 | nèi néng |
A gas can't make energy from nothing
- Heat a gas in a cylinder and it can push a piston, doing useful work.
- But it can only give out as much energy as it takes in — no more.
- Energy is conserved, even for jiggling gas particles.
- Bookkeeping that energy is the first law of thermodynamics 热力学第一定律.
气体无法凭空制造能量
- 加热气缸里的气体,它能推动活塞,做有用的功。
- 但它只能放出它所吸收的那么多能量——不会更多。
- 即使对乱窜的气体粒子,能量也守恒。
- 给这份能量记账,就是热力学第一定律。
The first law
- The internal energy 内能 $U$ of a gas is the total kinetic energy of its particles.
- The first law: $\Delta U = Q - W$.
- $Q$ is the heat added to the gas; $W$ is the work done by the gas.
- It is simply conservation of energy applied to a gas.
第一定律
- 气体的内能 $U$ 是其粒子的总动能。
- 第一定律:$\Delta U = Q - W$。
- $Q$ 是加给气体的热;$W$ 是气体所做的功。
- 它就是应用于气体的能量守恒。
Heat, work and internal energy · 热量、功和内能
Let the gas expand against a piston and see energy leave as work while heat flows in. · 让气体推动活塞膨胀，观察能量以功的形式流出，同时热量流入。
A gas absorbs $500\ \text{J}$ of heat and does $200\ \text{J}$ of work. What is its change in internal energy, in joules? · 一种气体吸收了 $500\ \text{J}$ 的热量并做了 $200\ \text{J}$ 的功。其内能的变化是多少，单位为焦耳？
$\Delta U = Q - W = 500 - 200 = 300\ \text{J}$.
The first law of thermodynamics is really a statement of: · 热力学第一定律实际上是关于____的陈述：
$\Delta U = Q - W$ is energy conservation applied to a gas. · $\Delta U = Q - W$ 是将能量守恒应用于气体的表述。
Where the energy goes
- Add heat and do no work: all of it raises the internal energy ($\Delta U = Q$).
- Let the gas expand and push a piston: some energy leaves as work, so $U$ rises less.
- Compress the gas (work done on it): its internal energy rises.
- The gas is just an energy account: heat in, work out, and what's left is $\Delta U$.
能量去了哪里
- 加热而不做功:全部用于抬高内能($\Delta U = Q$)。
- 让气体膨胀并推动活塞:一部分能量作为功离开,所以 $U$ 升得较少。
- 压缩气体(对它做功):它的内能升高。
- 气体就是一个能量账户:吸热、做功,剩下的就是 $\Delta U$。
A gas absorbs $400\ \text{J}$ of heat but does no work (rigid container). What is $\Delta U$, in joules? · 一种气体吸收了 $400\ \text{J}$ 的热量但未做功（刚性容器）。$\Delta U$ 是多少，单位为焦耳？
With $W = 0$, $\Delta U = Q = 400\ \text{J}$ — all the heat raises the internal energy. · 根据 $W = 0$，$\Delta U = Q = 400\ \text{J}$ —— 所有热量都增加了内能。
Internal energy and temperature
- For an ideal gas, internal energy depends only on temperature.
- More internal energy means faster particles, so a higher temperature.
- So $\Delta U > 0$ means the gas got hotter; $\Delta U < 0$ means it cooled.
- Heating without letting it expand is the fastest way to raise its temperature.
内能与温度
- 对理想气体,内能只取决于温度。
- 更多的内能意味着更快的粒子,所以温度更高。
- 所以 $\Delta U > 0$ 意味着气体变热了;$\Delta U < 0$ 意味着它变冷了。
- 加热而不让它膨胀,是抬高其温度最快的方式。
For an ideal gas, internal energy depends only on its . · 对于理想气体，内能仅取决于其。
Internal energy is the particles' kinetic energy, which tracks temperature. · 内能是粒子的动能，它与温度相关。
A positive $\Delta U$ for an ideal gas means the gas got hotter. · 对于理想气体，正的 $\Delta U$ 意味着气体变热了。
More internal energy means faster particles and a higher temperature. · 更多的内能意味着更快的粒子和更高的温度。
Watch the signs. $W$ in $\Delta U = Q - W$ is the work done by the gas (positive when it expands). Heat added is positive $Q$; heat removed is negative. Mixing up "work by" and "work on" the gas is the classic first-law error.
注意符号。$\Delta U = Q - W$ 中的 $W$ 是气体所做的功(膨胀时为正)。加入的热为正 $Q$;移除的热为负。把气体"做的功"和"对它做的功"弄混,是第一定律的经典错误。
In $\Delta U = Q - W$, select all · 所有 true statements about the signs. · 在 $\Delta U = Q - W$ 中，选择所有关于符号的正误描述。
$Q$ is heat added, $W$ is work by the gas (positive on expansion); compression does work on the gas, raising $U$. · $Q$ 是加入的热量，$W$ 是气体做的功（膨胀时为正）；压缩是对气体做功，从而提高 $U$。
A gas absorbs $500\ \text{J}$ of heat and does $200\ \text{J}$ of work pushing a piston out.
- $\Delta U = Q - W = 500 - 200 = 300\ \text{J}$.
The internal energy rises by $300\ \text{J}$, so the gas ends up hotter.
一团气体吸收 $500\ \text{J}$ 的热,并做 $200\ \text{J}$ 的功把活塞推出去。
- $\Delta U = Q - W = 500 - 200 = 300\ \text{J}$。
内能升高了 $300\ \text{J}$,所以气体最终变热了。
The first law of thermodynamics is conservation of energy for a gas: $\Delta U = Q - W$, where $Q$ is heat added and $W$ is work done by the gas. For an ideal gas, internal energy depends only on temperature, so $\Delta U > 0$ means it warmed up.
热力学第一定律是气体的能量守恒:$\Delta U = Q - W$,其中 $Q$ 是加入的热,$W$ 是气体所做的功。对理想气体,内能只取决于温度,所以 $\Delta U > 0$ 意味着它变热了。