定体, 定压, 定温, 绝热 Q E A 公式

• 通用: \(PV = \frac{M}{M_{mol}}RT = \gamma RT\)
  • \(M\): 质量
  • \(M_{mol}\): 1 mol物质的质量
  • \(\gamma\): 几摩尔
• 求内能变化: \(\triangle E = \gamma C_V \triangle T = \gamma\frac{i}{2}R\triangle T = \frac{i}{2}(P_2 V_2 - P_1 V_1)\)
  • \(C_v\): 等体摩尔热容
  • \(i\): 分子自由度
    • 单原子, \(i=3\)
    • 双原子, \(i=5\)
    • 多原子, \(i=6\)

1. \(\triangle V = 0, A = 0\)
   • \(\triangle E = \gamma C_V \triangle T = \gamma\frac{i}{2}R\triangle T = \frac{i}{2}(P_2 V_2 - P_1 V_1)\)
   • \(Q = \triangle E\)
2. \(\triangle P = 0\)
   • \(A = P\triangle V = \gamma R \triangle T\)
   • \(\triangle E = \gamma C_V \triangle T = \gamma\frac{i}{2}R\triangle T = \frac{i}{2}P\triangle V\)
   • \(Q = A + \triangle E = \gamma R \triangle T + \gamma\frac{i}{2}R\triangle T = \gamma\frac{2+i}{2}R\triangle T = \gamma C_P\triangle T = \frac{2+i}{2}P\triangle V\)
3. \(\triangle T = 0, \triangle E = 0\)
   • \(A = \int_{v1}^{v2}PdV = \int_{V_1}^{V_2}\frac{\gamma RT}{V}dV = \gamma RT\int_{V_1}^{V_2}\frac{dV}{V} = \gamma RT(ln{V_2} - ln{V_1}) = \gamma RT ln{\frac{V_2}{V_1}} = \gamma RT ln{\frac{P_1}{P_2}} = P_1V_1 ln{\frac{V_2}{V_1}} = P_2V_2 ln{\frac{P_1}{P_2}}\)
   • \(Q = A\)
4. \(Q = 0\)
   • \(\triangle E = \gamma C_V R\triangle T = \frac{i}{2}(P_2 V_2 - P_1 V_1)\)
   • \(A = Q - \triangle E = - \triangle E\)

定体, 定压, 定温, 绝热 Q E A 公式

原文：https://www.cnblogs.com/edhg/p/12148804.html