General calculation study method of thermodynamic functions for substances
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摘要: 物质热力函数（摩尔定压热容、熵、焓）是用于火箭发动机热力特性分析的常用函数.根据热力学关系，上述3种热力函数可表示为以温度为自变量，且含相同7个温度系数的多项式.由于精确分析物质热力特性的需要，需要各温度下更新更精确的数据值.将热力函数按温度高低分为不同区间，在保证各温度连接点函数值相等的情况下，采用最小二乘法的数学方法，通过编程计算，重新确定了135种火箭发动机常用物质的温度系数，得到300~ 5 000 K 内这些物质的函数计算值.进一步，对氮原子、液体铅、固体硅等相对误差较大的26种物质的摩尔定压热容利用最小二乘法再次进行了修正，使其精确度平均提高了100倍.所得到的热力函数计算值与标准值比较，误差小，精度高，使用方便，具有广泛的应用价值.Abstract: The substance's thermodynamic functions (heat capacity, entropy, enthalpy) were commonly used in the rocket engine's thermal property analysis. According to the thermodynamic relation, the three functions above can be expressed as polynomial on temperature with the same seven factors. Due to the technological progress, newer and more precious data at different temperatures were demanded. The function data were divided into different intervals based on temperatures, to ensure the calculated data were equal at adjacent intervals, with the least square method and program calculating, 135 kinds of substances' temperature coefficients were redefined. And the above substances' calculated thermodynamic functions from 300 K to 5 000 K were determined. Furthermore, to get more precise values, the heat capacities of 26 substances such as nitrogen atom, liquid lead, crystalline silicon, which had larger relative errors were corrected by using the least square method and the precision of heat capacities is 100 times higher than before. Compared with the standard data, the calculated data have small error and high precision and can be applied to many disciplines.
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Key words:
- thermodynamic function /
- least square method /
- temperature coefficient
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