等压过程
等压过程是压强不变的热力学过程:
。传递给一个系统的热量,既对它做功,又改变了系统的内能:
![](https://moenest.com/kexue/pic/4879a84a9874a13cdd076488920cdb40ab6b926d.svg)
热力学 |
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![](https://moenest.com/kexue/pic/Carnot_heat_engine_2.svg.png.webp) |
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比热容 |
![](https://moenest.com/kexue/pic/891d40a9b18752b04065caee655d008b3ec11428.svg) |
![](https://moenest.com/kexue/pic/ec7200acd984a1d3a3d7dc455e262fbe54f7f6e0.svg) | ![](https://moenest.com/kexue/pic/c609f4d3c5692ea4495479ef47594dc67f9fa464.svg) | ![](https://moenest.com/kexue/pic/f5e3890c981ae85503089652feb48b191b57aae3.svg) | ![](https://moenest.com/kexue/pic/504aa558fff3d00d10b03cadb1085cb0b7bdc631.svg) |
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压缩性 |
![](https://moenest.com/kexue/pic/b01c042bf1456bd4d2a8caed1f4912820a7ecbb3.svg) |
![](https://moenest.com/kexue/pic/92d98b82a3778f043108d4e20960a9193df57cbf.svg) | ![](https://moenest.com/kexue/pic/0cecdd9d069fa84159940068fc11a91b6b3b9ee4.svg) | ![](https://moenest.com/kexue/pic/af0f6064540e84211d0ffe4dac72098adfa52845.svg) | ![](https://moenest.com/kexue/pic/ebc4a48eb2412f08b54fe438b5139c88f9cfa372.svg) |
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热膨胀 |
![](https://moenest.com/kexue/pic/a92d4583d351f08c1c70985f0c843b2fff1b01e7.svg) |
![](https://moenest.com/kexue/pic/92d98b82a3778f043108d4e20960a9193df57cbf.svg) | ![](https://moenest.com/kexue/pic/0cecdd9d069fa84159940068fc11a91b6b3b9ee4.svg) | ![](https://moenest.com/kexue/pic/af0f6064540e84211d0ffe4dac72098adfa52845.svg) | ![](https://moenest.com/kexue/pic/504aa558fff3d00d10b03cadb1085cb0b7bdc631.svg) |
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内能![](https://moenest.com/kexue/pic/921f33f9c6551562ec836007b035c2de6323d2d6.svg)
焓![](https://moenest.com/kexue/pic/6407d78e5f39d07f70e2414a92e08e2e068519f3.svg)
亥姆霍兹自由能![](https://moenest.com/kexue/pic/5e93692f031ba6484d82731c54db83a69daed3f0.svg)
吉布斯能![](https://moenest.com/kexue/pic/8dd7a8f0b8ae04963da133e3b202432e1b6caed4.svg)
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![](https://moenest.com/kexue/pic/Isobaric_process_plain.svg.png.webp)
黄色部分的面积表示所做的功
根据热力学第一定律,其中W是系统所做的功,U是内能,Q是热量。系统所做的压强-体积功,定义为:(Δ表示整个过程中的变化,不是微分的意思)
![](https://moenest.com/kexue/pic/62fbe3896d082fce41acfa811736a8afa1acfc48.svg)
由于压强是常数,因此
.
应用理想气体状态方程,等式变为
![](https://moenest.com/kexue/pic/da82aa292dc47ab00bf5f721416f74540ea636fc.svg)
假设气体的质量是不变的。由于:
![](https://moenest.com/kexue/pic/2633a5921ce8bf7f5d51f5e90adde289c0426cb2.svg)
其中n是物质的量,cV是等容摩尔热容。把最后两个方程代入第一个方程,得
![](https://moenest.com/kexue/pic/807ba6696ac0197ad0da29076190f44c244c8e5f.svg)
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括号中的表达式是等压摩尔热容:
![](https://moenest.com/kexue/pic/eff3e5a0d218065f297e85dd8cc2e6ec898505d2.svg)
等压过程在P-V图中是一条水平直线。如果方向是朝右面的,则过程是等压膨胀。如果方向是朝左面的,则过程是等压收缩。
焓的定义
等容过程由方程
描述。对于等压过程也有类似的方程。把第二个方程代入第一个方程,得
![](https://moenest.com/kexue/pic/620c2ae6afe259c02ca414ea5d7175c438eb8d62.svg)
U + p V是一个状态函数,称为焓,用字母H表示。所以等压过程可以表示为:
.
参见