A diesel engine takes in air ($\gamma$ = 1.4)at 20 $\circ$ C and compresses it adiabatically to 1/10 of its original volume.The final temperature of the air is

Question

Quizplus · Accepted Answer

Using the adiabatic compression formula:

(P1/P2)^((γ-1)/γ) = (T2/T1)

where P is pressure and T is temperature, and γ is the ratio of specific heats.

Firstly, convert the temperature in Celsius to Kelvin:

T1 = 20°C + 273.15 = 293.15 K

Since the compression ratio is 1/10, the final pressure is 10 times the initial pressure:

P2 = 10P1

Plugging in the values, we get:

(10)^((1.4-1)/1.4) = (T2/293.15)

Simplifying, we get:

T2 = 463.15 K

Therefore, the final temperature is 463°F.

A Diesel Engine Takes in Air γ\gammaγ = 14)at 20 ∘\circ∘

A Diesel Engine Takes in Air $\gamma$ = 14)at 20^$\circ$