The Ideal Gas Law · 理想气体定律
| English | 中文 | Pinyin · 拼音 |
|---|---|---|
| ideal gas law/aɪˈdɪəl ɡæs lɔː/ | 理想气体定律 | lǐ xiǎng qì tǐ dìng lǜ |
Pump up a tyre — it gets hot and hard
- Push a bike pump and the barrel warms up while the tyre grows firm.
- You squeezed the gas into less space, and its pressure and temperature climbed.
- One tidy equation ties pressure, volume, temperature and amount of gas together.
- It is the ideal gas law 理想气体定律, the workhorse of thermodynamics.
给轮胎打气——它变热又变硬
- 推自行车打气筒,筒身发热,而轮胎变硬。
- 你把气体挤进更小的空间,它的压强和温度都升高了。
- 一个简洁的方程把压强、体积、温度和气体的量联系在一起。
- 它就是理想气体定律,热力学的主力。
The equation
- The ideal gas law is $PV = nRT$.
- $P$ is pressure, $V$ volume, $n$ the amount of gas (in moles), $T$ the kelvin temperature.
- $R$ is the universal gas constant, the same for every ideal gas.
- Know any three of $P, V, T$ (for fixed $n$) and the fourth is fixed.
方程
- 理想气体定律是 $PV = nRT$。
- $P$ 是压强,$V$ 是体积,$n$ 是气体的量(以摩尔计),$T$ 是开尔文温度。
- $R$ 是普适气体常数,对每种理想气体都相同。
- 知道 $P, V, T$ 中的任意三个(在 $n$ 固定时),第四个就确定了。
Squeeze the gas · 压缩气体
Change the volume and watch the pressure respond along an isotherm — PV stays constant. · 改变体积并观察压强沿等温线如何响应——PV保持恒定。
Which is the ideal gas law? · 哪个是理想气体定律？
$PV = nRT$ links pressure, volume, amount and temperature. · $PV = nRT$ 将压强、体积、物质的量和温度联系起来。
In $PV = nRT$, the symbol $n$ is the amount of gas measured in ____. · 在 $PV = nRT$ 中，符号 $n$ 代表以____为单位测量的气体量。
$n$ is the number of moles of gas. · $n$ 表示气体的摩尔数。
The relationships inside it
- At constant temperature, $P$ and $V$ are inversely related: squeeze $V$, and $P$ rises.
- At constant volume, $P$ rises in proportion to the kelvin temperature.
- At constant pressure, volume rises in proportion to temperature.
- Each is a special case of the one master equation $PV = nRT$.
其中蕴含的关系
- 在恒温下,$P$ 与 $V$ 成反比:压缩 $V$,$P$ 就升高。
- 在恒容下,$P$ 与开尔文温度成正比升高。
- 在恒压下,体积与温度成正比升高。
- 每一个都是那一个主方程 $PV = nRT$ 的特例。
A gas at $100\ \text{kPa}$, $2\ \text{m}^3$ is squeezed to $0.5\ \text{m}^3$ at constant temperature. What is the new pressure, in $\text{kPa}$? · 一种处于 $100\ \text{kPa}$、$2\ \text{m}^3$ 的气体在恒温下被压缩至 $0.5\ \text{m}^3$。新压强是多少，单位为 $\text{kPa}$？
$P_1V_1 = P_2V_2 \Rightarrow 200 = 0.5 P_2 \Rightarrow P_2 = 400\ \text{kPa}$.
At constant temperature, if you halve a gas's volume, its pressure: · 在恒温条件下，如果你将气体的体积减半，其压强会：
$PV$ is constant, so halving $V$ doubles $P$. · $PV$是恒定的，因此将$V$减半会使$P$加倍。
A gas at $300\ \text{K}$ has pressure $200\ \text{kPa}$ in a rigid container. Heated to $600\ \text{K}$, what is its new pressure, in $\text{kPa}$? · 一种处于 $300\ \text{K}$ 的气体在刚性容器中压强为 $200\ \text{kPa}$。加热到 $600\ \text{K}$ 后，其新压强是多少，单位为 $\text{kPa}$？
At constant volume, $P \propto T$: doubling the kelvin temperature doubles the pressure to $400\ \text{kPa}$. · 在恒容条件下，$P \propto T$：将开尔文温度加倍会使压强加倍至 $400\ \text{kPa}$。
When it works
- The law is exact for an ideal gas — particles with no size and no forces between them.
- Real gases follow it closely at ordinary pressures and well above their boiling point.
- It breaks down near condensation, where particle forces matter.
- For AP problems, treat gases as ideal unless told otherwise.
它何时成立
- 该定律对理想气体是精确的——粒子没有大小、彼此之间没有力。
- 真实气体在普通压强下、并远高于其沸点时紧密遵循它。
- 它在接近凝结时失效,那里粒子间的力起作用。
- 对 AP 问题,除非另有说明,把气体当作理想气体。
Temperature in the ideal gas law must be in kelvin. · 理想气体定律中的温度必须使用开尔文单位。
The law is proportional in kelvin; using $^\circ\text{C}$ gives wrong ratios. · 该定律在开尔文温标下才成立；使用 $^\circ\text{C}$ 会导致错误的比例关系。
Always put temperature in kelvin in $PV = nRT$. Using $^\circ\text{C}$ gives nonsense — for example, "doubling from $10\,{}^\circ\text{C}$ to $20\,{}^\circ\text{C}$" is not doubling the temperature ($283\ \text{K}$ to $293\ \text{K}$ is only a $3.5\%$ rise).
在 $PV = nRT$ 中,温度总要用开尔文。用 $^\circ\text{C}$ 会得到荒谬的结果——例如"从 $10\,{}^\circ\text{C}$ 到 $20\,{}^\circ\text{C}$ 加倍"并不是温度加倍($283\ \text{K}$ 到 $293\ \text{K}$ 只升高了 $3.5\%$)。
A gas at pressure $100\ \text{kPa}$ and volume $2\ \text{m}^3$ is squeezed to $0.5\ \text{m}^3$ at constant temperature. Find the new pressure.
- At constant $T$, $P_1 V_1 = P_2 V_2 \Rightarrow 100 \times 2 = P_2 \times 0.5$.
- $P_2 = \dfrac{200}{0.5} = 400\ \text{kPa}$ — four times larger, as the volume shrank fourfold.
一团压强 $100\ \text{kPa}$、体积 $2\ \text{m}^3$ 的气体在恒温下被压缩到 $0.5\ \text{m}^3$。求新的压强。
- 在恒 $T$ 下,$P_1 V_1 = P_2 V_2 \Rightarrow 100 \times 2 = P_2 \times 0.5$。
- $P_2 = \dfrac{200}{0.5} = 400\ \text{kPa}$——大了四倍,因为体积缩小了四倍。
The ideal gas law is $PV = nRT$ (temperature in kelvin). At constant $T$, $P$ and $V$ are inversely related ($P_1V_1 = P_2V_2$); at constant $V$ or $P$, the others rise with temperature. It holds well for real gases away from condensation.
理想气体定律是 $PV = nRT$(温度用开尔文)。在恒 $T$ 下,$P$ 与 $V$ 成反比($P_1V_1 = P_2V_2$);在恒 $V$ 或恒 $P$ 下,其余量随温度升高。它对远离凝结的真实气体也很好地成立。