Engine Temperature

Question

In an engine, air is at 1x10²kpa and a temperature of 298.15K in a cylinder volume of 0.400L. The air is then compressed to 0.050L volume and pressure of 2.5x10³kpa. Assume number of moles is constant. 

 

a) what is the temperature of the compressed air in Kelvins? 

Answer 1

I will set this up for you, and you can finish the solution.

 

Assuming it is an ideal gas, then at constant amount of gas (i.e. at constant number of moles),

 

PV/T = constant

 

P₁V₁/T₁ = P₂V₂/T₂

 

T₂ = T₁(P₂V₂)/(P₁V₁)

 

T₁ = 289.15 K

P₁ = 1 x 10² kPa

V₁ = 0.400 L

P₂ = 2.5 x 10³ kPa

V₂ = 0.050 L

 

Just substitute these values into the equation for T₂ to get the final temperature.  Can you take it from here?