Question

A single cylinder petrol engine has a volume compression ratio of 4:1, takes in a mixture of fuel and air at a temperature of 20°Cand its pressure is 101kPa. If the pressure at the end of the compression stroke is 1.5MPa what will be its final temperature?

Answer 1

The problem involves an adiabatic compression, therefore the governing equation will be 

$\frac{V_2}{V_1}=\frac{1}{4}$ $P_1=101kPa=0.101\times{10}^6 Pa T_1=20 C = 293.15 K P_2=1.5 MPa=1.5\times{10}^6Pa$

$P*V^k = constant$

and also, $T* V^{k-1} = constant$

Considering two states, using the first equation:

0.101\times{10}^6\times4^k=1.5\times{10}^6\times1 =>4^k=14.81=>\ k\cong\ 1.944\

Now it’s possible to use the second equation 

$T_1\times{V_1}^{k-1}=T_2\times{V_2}^{k-1} \\ 293.15\times4^{0.944}=T_2\Rightarrow \\T_2=1085.01\ K\ =811.86\ C$