Answer to Question #115779 in Mechanical Engineering for Smith

Question

Air initially at 15 psia and 60 0F is brought to a final temperature of 200 0F by a reversible non-flow process. Correlate with problem 7, show the processes on the p-V and T-s diagram and find the heat transferred in BTU/lb if a.) n=0, b.)n=∞, c.) n=k and n=1.2.

Answer 1

In the polytropic process

$q_p=c_v\frac{n-k}{n-1}(T_2-T_1)$

So, we have

(a) $n=0$

$q=c_v\cdot\frac{c_p}{c_v}\cdot (T_2-T_1)=c_p\cdot (T_2-T_1)=0.239\cdot(200-60)=33.46 BTU/lb$

(b) $n=\infin$

$q=c_v\cdot(T_2-T_1)=0.171\cdot(200-60)=23.94BTU/lb$

(c) $n=k$

$q=0$

(d) $n=1.2$

$q=c_v\frac{n-k}{n-1}(T_2-T_1)=0.171\cdot\frac{1.2-0.239/0.171}{1.2-1}(200-60)=-23.66BTU/lb$