Adiabatic Process for an Ideal Gas

[cmilho10]

During the compression stroke of a certain gasoline engine, the pressure increases from 1.00 atm to 20.3 atm. Assume that the process is adiabatic and the gas is ideal with (gamma)= 1.40.

(a) By what factor does the volume change?
Vfinal = (ans)*Vinitial
(b) By what factor does the temperature change (when expressed using an absolute scale)?
Tfinal =(ans) * Tinitial
(c) If the compression starts with 0.0160 mole of gas at 27.5°C, find the values of Q, W, and Eint that characterize the process.

I know the relationship is described by PV^(gamma)=constant but am clueless on how to apply this to get the answers.

 

[Gamma]

pv ^ gamma = constant means you can write

Pi Vi ^gamma = Pf Vf^gamma. You need to simply rearrange this equation to get Vi/Vf.

for part b:

From PV = nRT, you can write Pi Vi/Ti = Pf Vf /Tf

Since you already know Pi/Pf and Vi/Vf, rearrange the above to get Ti/Tf.

For part c.

If i remember correct for adiabetic process, Q=0. So change in internal energy, dE = dW

and work done on the system W = -intgration (dW) = -intgration (PdV)
where P= nRT/V


Limit of integration is Vi to Vf. You will have to use the given info about mole number and temperature to find vi and vf.