A 13 gram sample of an unknown metal at 26.5°C is placed in a Styrofoam cup containing 50.0 grams of water at 88.6°C. The water cools down and the metal warms up until thermal equilibrium is achieved at 87.1°C. A 10 percent of heat lost by water is transferred through the cup, determine the specific heat capacity of the unknown metal. The specific heat capacity of water is 4.18 J/g/°C.

Answer 1

The sums of heats gained in the system is zero.

heatgained by water*.9+heatgainedmetal=0
notice the .9 to inidcated the 90 percent efficiency.

50*cw*(87.1-88.6).9+13Cm*(87.1-26.5)=0

solve for Cm