Question

An air-standard Otto cycle has a compression ratio of 8, and the temperature and pressure at the beginning of the compression process are 520°R and 14.2 lbf/in.2, respectively. The mass of air is 0.0015 lb. The heat addition is 0.9 Btu. Determine (a) the maximum temperature, in °R. (b) the maximum pressure, in lbf/in.2 (c) the thermal efficiency

Answer 1

a)
`T_3=4194.64R`

b)
`P_3=916.21lbf/in^2`

c)
`\eta=0.56`

Step-by-step explanation:

Given that

Compression ratio(r)=8

We know that
`r=(V_1)/(V_2)`

`P_=14.2lbf/in^2,T_1=520R`

mass of air =0.0015 lb

Heat addition=0.9 btu

`T_2=r^(\gamma-1)T_1`

So

`T_2=8^(1.4-1)* 520`

`T_2=1194.64R`

To find maximum temperature

We know that heat added at constant volume in petrol cycle

`Q=mC_v(T_3-T_2)`

`0.9 =.0015* (T_3-T_2)* 0.21`

`0.9 =.0015* (T_3-1194.64)* 0.21`

`T_3=4194.64R`

To find maximum pressure

`P_2=r^(\gamma)P_1`

`P_2=8^(1.4)* 14.2`

`P_2=260.98lbf/in^2`

`(P_3)/(P_2)=(T_3)/(T_2)`

So
`P_3=916.21lbf/in^2`

To find efficiency

`\eta =1-(1)/(r^(\gamma-1))`

`\eta =1-(1)/(8^(1.4-1))`

`\eta=0.56`