Answer:
Net work, W = 842.52 kJ/kg
Power, P = 32.82 kW
Given:
compression ratio, r = 10:1
Total volume displaced,
![V_(d) = 2.3 l = 2.3* 10^(- 3) m^(3)](https://img.qammunity.org/2020/formulas/engineering/college/p7pmyvasfyogsf19hnuo6ffh3sbjdssy5i.png)
= 280 K
= 70 kPa
Speed, N = 2100 rpm = 35 rps
Heat energy added, Q = 1400 kJ/kg
Solution:
Now, calculation of the overall efficiency:
![\eta = 1- r^(1 - k)](https://img.qammunity.org/2020/formulas/engineering/college/9o9s8kc9mg4h298t4dj5f6gic7odagxxxj.png)
where
k = 1.4
![\eta = 1- 10^(0.4) = 0.6018](https://img.qammunity.org/2020/formulas/engineering/college/ts3htip4j55k8uh5dprk56vrhrztmkmtx1.png)
Also,
Net work done, W =
![\eta Q = 0.6018* 1400 = 842.52 kJ/kg](https://img.qammunity.org/2020/formulas/engineering/college/9ohv8x35yq1rkudglc9xjeeiz3c923dx60.png)
Now, specific volume is given by:
![P_(inlet)\vartheta = RT_(inlet)](https://img.qammunity.org/2020/formulas/engineering/college/jx92p12o99et5t288ajm2vbko3zw2f336j.png)
![70* 10^(3)\vartheta = 0.287* 280](https://img.qammunity.org/2020/formulas/engineering/college/mw26dntg6gdk4navvhiyevjyjyxt7p7kxn.png)
![\vartheta = 1.148 m^(3)/kg](https://img.qammunity.org/2020/formulas/engineering/college/9xc45d94uzqvke5jkq5x5bxu4pqjc5et5h.png)
Now, mean effective pressure, P' can be calculated as:
![W = P'(\vartheta - \vartheta')](https://img.qammunity.org/2020/formulas/engineering/college/tssj97dnwwytnvj5vtybn9o7wq0fxi1x7r.png)
![(W)/((\vartheta - \vartheta')) = P'](https://img.qammunity.org/2020/formulas/engineering/college/p4y4xlhi65i49xfyzpbtvoq7at8ct0600x.png)
![(842.52)/(\vartheta(1 - (\vartheta')/(\vartheta))) = P'](https://img.qammunity.org/2020/formulas/engineering/college/fai608qhgc7s2zcvs9z2biorkf3c1uzgu6.png)
(Since, r =
)
![(842.52)/(\vartheta(1 - (1)/(r))) = P' = (842.52)/(1.148(1 - (1)/(10)))](https://img.qammunity.org/2020/formulas/engineering/college/mygu2wgvstlapfioshj6ghoniv8qguginv.png)
P' = 815.45 kPa
Now, for power produced, P:
P =
![(1)/(2)P'V_(d) N](https://img.qammunity.org/2020/formulas/engineering/college/m6ksa8bhxfnngvii13riu1cnut7zsn2z5y.png)
P =
![(1)/(2)* 815.45* 2.3\time 10^(- 3)* 35](https://img.qammunity.org/2020/formulas/engineering/college/gd3oj69ip93f21j5bjd2o5g7kt7u3vv4h4.png)
P = 32.82 kW