(1) 앞선 "거거"님의 답변대로 부피의 단위가 모두 표준상태의 부피 즉 Nm3/min라고 가정 하면 부피는 그냥 덧셈이 가능합니다. 부피가 표준상태 부피로 환산되어 있기 때문에 전체부피 = 450 Nm3 + 550 Nm3 = 1000 Nm3./min 로 계산되지만 온도계산이 잘 못되어 있습니다.
40~800도에서의 공기의 평균 비열이 같다고 하여도 다음과 같은 수식으로 온도를 계산해야 합니다.
혼합가스의 온도 T라고 하면 (찬공기가 얻은열) = (고온공기가 잃은열)
(450 Nm3/min)*Cpm1*(T-40)℃ = (550 Nm3/min)*(Cpm2*(800-T) .....................(1)
이로부터 계산하면 T = (450*40)+(550*800)/(1000) = 458 ℃ ..................................(2)
이 계산에는 40~T도에서의 평균 비열 Cpm1과 800~T도까지의 평균비열 Cpm2가 같다고 가정했을 대 (2)식이 되지만 평균비열이 다르다면 Cpm1, Cpm2값을 실제로 넣어주어야 합니다.
(2) 만일 부피가 각각의 온도에서의 부피라고 하면 이를 모두 표준상태의 부피로 환산해서 계산해야 합니다 압력은 대기압이라고 가정하고 각각의 부피는
(5) 질문의 문제에 대해 엄밀한 계산이라고 하면 (5)식을 적용해야 합니다. 그러나 최종온도 T를 아직 모르기 때문에 (5)식과 (1)식을 이용해서 시행오차방법을 이용해서 계산해야 합니다. 즉
T를 가정하고 Cpm1과 Cpm2를 계산한다음 (1)식에 넣어 가정한 T와 같아지면 T가 맞습니다.
수계산으로 할 때는 위에서 비열이 같다고 계산한 458도로부터 시작하면 2~3번 만에 거의 비슷하게 맞출 수 있습니다.
이런 계산은 수계산으로 하면 어렵지만 엑셀이나 수학전용 도구를 이용하면 쉽게 계산이 됩니다.
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