First slide

Heat Engine; Carnot Engine and refrigerator

Question

A gas has $γ$ =4/3 and is heated at constant pressure, what percentage of total heat supplied is used for doing external work:

Moderate

A

25%
B

20%
C

10%
D

5%

Solution

$\begin{array}{rcl} g i v e n s p e c i f i c h e a t r a t i o & = & γ = \frac{C_{p}}{C_{v}} = \frac{4}{3} \\ t o t a l h e a t s u p p l i e d & = & ∆ Q = n C_{p} ∆ T \\ e x t e r n a l w o r k d o n e & = & ∆ W = n R ∆ T \\ p e r c e n t a g e o f t o t a l h e a t s u p p l i e d i n d o i n g e x t e r n a l w o r k & = & \frac{∆ W}{∆ Q} x 100 \\ = & \frac{n R ∆ T}{n C_{p} ∆ T} x 100 \\ = & \frac{R}{C_{p}} x 100 \\ = & \frac{C_{p} - C_{v}}{C_{p}} x 100 \\ = & (1 - \frac{1}{γ}) 100 \\ = & (1 - \frac{1}{\frac{4}{3}}) 100 \\ = & (1 - \frac{3}{4}) 100 \\ = & \frac{1}{4} x 100 \\ = & 25 % \end{array}$

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