2. A closed system of air (with molecular weight of Wair and constant specific heat capacity cp and

cv) in the cylinder of a compression ignition (CI) engine undergoes polytropic compression

during which the volume decreases 10 times, and the pressure increases 32 times. If the initial

pressure and specific volume are p₁ and v₁, determine the mathematical expression for (show

the details of your work)

a. The polytropic index of the compression process

b. Temperature of the air at the end of compression

c. Compression work

d. Change of internal energy

e. Heat added to the process