With adiabatic compression of air in the cylinders of an internal combustion engine

With adiabatic compression of air in the cylinders of an internal combustion engine, the pressure changes from 0.1 MPa to 3.5 MPa. initial air temperature 40C. find the air temperature at the end of the compression stroke.

Given:

P1 = 0.1 MPa = 0.1 * 10 ^ 6 Pascal – pressure at the beginning of the cycle;

P2 = 3.5 MPa = 3.5 * 10 ^ Pascal – pressure at the end of the stroke;

i = 5 is the number of degrees of freedom for air;

T1 = 40 degrees Celsius = 313 degrees Kelvin – the initial air temperature.

It is required to determine T2 (degree Kelvin) – the final air temperature.

Since, according to the condition of the problem, the compression process occurs during adiabatic compression, then:

Let us find the adiabatic exponent:

y = (i + 2) / i = 1.4.

Find the degree:

n = (1 – y) / y = (1 – 1.4) / 1.4 = -0.4 / 1.4 = -0.3.

Then:

P1 ^ n * T1 = P2 ^ n * T2, hence:

T2 = P1 ^ n * T1 / P1 ^ n = 100000 ^ -0.3 * 313/3500000 ^ -0.3 = 0.03 * 313 / 0.01 =

= 9.39 / 0.01 = 939 Kelvin = 666 Celsius.

Answer: the air temperature at the end of compression will be 666 degrees Celsius.