The ideal gas law for an adiabatic process

1. The problem statement, all variables and given/known data

Hi can someone please have a look at this question and let me know if I am on the right track, thanks.

A diesel engine requires no spark plug; instead the air in the cylinder is compresses so highly the fuel ignites spontaneously on injection to the cylinder.

Q. If the air is initially at 293K and then is compressed adiabatically by a factor of 15, what final temperature is attained ?( Just prior to injection, also consider air as an ideal gas)
Variables:
T1=293K
V1= 1
V2=1/15
T2=?

2. Relevant equations

T1 *V1^(Ƴ-1) = T1* V1^(Ƴ-1)

3. The attempt at a solution
Above relationship applies as process is adiabatic?

293× (1^(1.4-1)/ (1/15^(1.4-1) ))=866K

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