严格证明克劳修斯等式的一种可行方法

A Practicable Way to Prove Clausius Equality Strictly

论述了一种从数学上严格证明克劳修斯等式的新方法,指出可逆循环热温比积分的数学实质是第二类曲线积分,并通过格林公式和能态方程证明了克劳修斯等式,最后指出了克劳修斯熵的引入数学上等价于寻找到一个合适的积分因子.

In this work,a vigorous mathematic proof of the Clausius equality is discussed.It is pointed out that the mathematical essence of the integral of heat temperature ratio in any reversible cycle is the second type of curve integral.The Clausius equality can be proved in terms of Green′s formula and energy state equation.Moreover,we suggest that the introduction of Clausius entropy is mathematically equivalent to finding a suitable integration factor.