A stream of n$-$butane enters a heat exchanger operating at $T_1=50C.$ The HEX operates at atmospheric pressure and $15,000\frac{J}{g}$mol are transferred to the substance.

Determine:

$3\mathrm{.}1$ Write the equation to calculate the outlet temperature $T_2.$ Use the information given in the table.

$3\mathrm{.}2$ Based on the previous equation find $T_2$ using the Newton$-$Raphson Method.

Use tolerance $=1{10}^{-4}$ Assume an initial value $T_{20}=300C$