Explanation:
It is given that,
Initial temperature, [tex]T_1=25^{\circ}C=298\ K[/tex]
Pressure, [tex]P_1=100\ kPa=10^5\ Pa[/tex]
Compression ratio, [tex]r=\dfrac{V_1}{V_2}=9.058[/tex]
Let T₂ is the final temperature of air. Using the relation for reversible adiabatic process as :
[tex]\dfrac{T_2}{T_1}=(\dfrac{V_1}{V_2})^{\gamma-1}[/tex]............(1)
Where,
[tex]\gamma=\dfrac{C_p}{C_v}[/tex]
For air, [tex]C_p=1.004[/tex] and [tex]C_v=0.717[/tex]
[tex]\gamma=1.4[/tex]
So, equation (1) becomes :
[tex]T_2=T_1\times (\dfrac{V_1}{V_2})^{\gamma-1}[/tex]
[tex]T_2=298\times (9.058)^{1.4-1}[/tex]
[tex]T_2=719.49\ K[/tex]
So, the final temperature of air is 719.49 K. Hence, this is the required solution.
