How do you get the answer for this adiabatic compression?

in adiabatic compression

TV^(γ-1)=constant

then

T1V1^(γ-1)=T2V2(γ-1)

T2/T1=V1^(γ-1)/V2^(γ-1)=(V1/V2)^(γ-1)

T2/T1=8^(2/3)

T2/T1=4

You use the fact that PV^gamma is a constant for an ideal gas in an adiabatic situation.

P1V1^gamma = P2V2^gamma

Solve for the new pressure, then use the ideal gas law to find the temperature.

There's a calculator on this page:

http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/...

Hello ? : You have for adiabatic and reversible compression of and Ideal Gas with

constant specific heats :

-----------------------------------

Q = 0.0

delta S = 0.0 ( isentropic )

( P ) ( V )^k = Constant

( T ) ( V )^k - 1.0 = Constant

k = Cp / Cv = gamma = 5 /3 = 1.667 ( in this istuation)

V1 / V2 = volume compression ratio = Rvks = 8.000

( T1 ) ( V1 )^1.667 - 1.0 = ( T2 ) ( V2 )^1.667 - 1.0

T2 = ( T1 ) ( V1 / V2 )^1.667 - 1.0

T2 = ( T1 ) ( 8 )^1.667 - 1.0

T2 = ( T1 ) ( 4.000 )

The temperature ratio is increased by a factor of 4.000 <------------------------------