任意可逆循環(huán)的熱溫比的和為零

1、任意可逆循環(huán)的熱溫比的和為零第1頁，共13頁，2022年，5月20日，14點(diǎn)15分，星期日In studying the efficiency of a Carnot engine we learned that if an ideal engine absorbs an amount of heat Qi at temperature Ti and then discards heat Qo at To , the quantities are related by or1. Energy and entropyIf we adopt the convention that the heat

2、 extracted is negative and heat input is positive , then the above relation becomes :P 330 - 334第2頁，共13頁，2022年，5月20日，14點(diǎn)15分，星期日An arbitrary reversible cycle can be approximated by a series of Carnot cycles . For each of the small Carnot cycle , we know that :Summing over all the isothermal paths alo

3、ng which heat Qj is either absorbed or rejected at temperature Tj , we obtain :任意可逆循環(huán)的熱溫比的和為零第3頁，共13頁，2022年，5月20日，14點(diǎn)15分，星期日By letting the heat become arbitrarily small , the sum approaches an integral For an reversible cycle , the line integral taken around a complete cycle is zero . In the other w

4、ords , for an reversible cycle the line integral between two states depends only on those states not on the path connecting them .可逆循環(huán)熱溫比的積分與路徑無關(guān)第4頁，共13頁，2022年，5月20日，14點(diǎn)15分，星期日To understand why the line integral is independent of the path , consider the system moving reversibly along path R1 from A

5、to B , then back to A along a different reversible path . We haveBecause each path is reversibleso that 證明可逆循環(huán)熱溫比的積分與路徑無關(guān)第5頁，共13頁，2022年，5月20日，14點(diǎn)15分，星期日In a reversible process , the line integral is independent of the path , therefore , it has physical significance . The line integral is called the

6、change in entropy between any two states A and B connected by a reversible process .由于任意可逆循環(huán)的熱溫比的積分與路徑無關(guān)，將這個積分叫做熵變。熵是狀態(tài)參量，熵與能量同樣重要。第6頁，共13頁，2022年，5月20日，14點(diǎn)15分，星期日What is the change in entropy for an irreversible process ?An irreversible process can not be represented by a continuous path on a PV dia

7、gram because it does not move through a series of equilibrium states . However , we can join the ends of an irreversible process on a PV diagram by a reversible process , then approximate the entire cycle by a series of small cycle .不可逆過程的熵變？第7頁，共13頁，2022年，5月20日，14點(diǎn)15分，星期日For an irreversible cycleor

8、Summing over all such cycles , and passing to the limit we obtain ：This equation means that in any irreversible process the entropy of an isolated system always increase .不可逆過程的熵總是增加的第8頁，共13頁，2022年，5月20日，14點(diǎn)15分，星期日Consider a irreversible process shown in the diagram .ororso證明不可逆過程的熵總是增加的第9頁，共13頁，202

9、2年，5月20日，14點(diǎn)15分，星期日For an isolated system , the entropy of the system increases after any irreversible process .The second law of the thermodynamics can be cast into another form : The entropy of the universe always increases towards a maximum .第10頁，共13頁，2022年，5月20日，14點(diǎn)15分，星期日heat death theory （熱寂說）

10、不論是星星還是太陽將來再升起，到處是一片黑暗， 沒有溪流的潺潺聲， 沒有聲音，沒有景色， 既沒有冬天的落葉， 也沒有春天的嫩芽， 沒有白天，也沒有勞動的歡樂， 在永恒的黑夜里， 只有沒有盡頭的夢鏡。英國詩人史文明這樣描述熱寂現(xiàn)代宇宙論的觀測與研究表明，宇宙正在膨脹，它不是趨于平衡，而是越來越不趨于平衡。熱力學(xué)第二定律在此不成立。第11頁，共13頁，2022年，5月20日，14點(diǎn)15分，星期日Example 1 An ideal gas is allowed to expand freely and adiabatically from a volume V1 to a volume V2 .

11、What is the change in entropy for this irreversible process ? ( A free expansion is one in which no work is done . )P 335We compute the change in entropy by considering a reversible process connecting the two states : a quasi - static isothermal expansion from V1 to V2 at constant temperature .第12頁，共13頁，2022年，5月20日，14點(diǎn)15分，星期日P 337Example 2 A copper wire connected between two large pieces of metal conducts 40J of heat from one piece at 400K to the other at 350K . What is the change in entropy for