I have a copper pipe. Volume is 47.768 cc copper @ 20 C. I pour in 237.61 cc (H2O)@71 C. How do I compute equalibrium temp?

use density of Cu to calculate mass.

then use specific heat of Cu x mass x (T–20) to get energy

use density of water to calcu mass.

then use specific heat of water x mass x (71–T) to get energy

set the two equal and solve for T

(you did ask "how", not for the solution)

assuming that volume for Cu is the actual Cu, not the volume of the pipe including interior.