Question

Air compressed in car engine from 25 C and 100 kPa in reversible and adiabatic manner. If the compression ratio = 9.058, determine final temperature of air.

Answer 1

Step-by-step explanation:

It is given that,

Initial temperature,
`T_1=25^(\circ)C=298\ K`

Pressure,
`P_1=100\ kPa=10^5\ Pa`

Compression ratio,
`r=(V_1)/(V_2)=9.058`

Let T₂ is the final temperature of air. Using the relation for reversible adiabatic process as :

`(T_2)/(T_1)=((V_1)/(V_2))^(\gamma-1)`............(1)

Where,

`\gamma=(C_p)/(C_v)`

For air,
`C_p=1.004` and
`C_v=0.717`

`\gamma=1.4`

So, equation (1) becomes :

`T_2=T_1* ((V_1)/(V_2))^(\gamma-1)`

`T_2=298* (9.058)^(1.4-1)`

`T_2=719.49\ K`

So, the final temperature of air is 719.49 K. Hence, this is the required solution.