Question $1(25$ points$)$

Measured data for pressure versus volume during the expansion of gases within the cylinder

of an internal combustion engine are given in the table below. Using data from the table,

complete the following:

$($a$)$ Determine a value of $n$ such that the data are fit by an equation of the form, $p{V}^n=$

constant.

$($b$)$ Evaluate analytically the work done by the gases, in kJ$,$ using Eq$.2\mathrm{.}17$ along with the

result of part $($a$).$

Unit conversion factors: $1kJ=1000N*m,\frac{1}{b}ar={10}^5\frac{N}{m^2},1m^3={10}^{6}c{m}^3.$