Problem $1.$ The specific heat Cv is the amount of heat required to raise the temperature of a given mass

of gas with constant volume by $1$C and is measured in units of cal$/$deg$-$mole $($calories per degree gram

molecule$).$ The specific heat of oxygen depends on its temperature T as satisfies the formula

Cv $=8\mathrm{.}27+105$

$26$T $1\mathrm{.}87$T

$2$

$.$

$($a$)$ Find the average value of Cv for $20$ T $675$C$.$ Set up the appropriate integral and compute the

average value by hand. You can use a simple calculator to help you, but you must compute the integral.