Madeline K. answered • 10/05/21
B.A. in Chemistry with 3+ years of Tutoring Experience
Hey! I don't answer student homework questions directly, but I can tell you about how to think about the problem and what steps would be helpful to solve it.
-First recall that the definition of specific heat: specific heat is the heat required to raise the temperature of one mass unit (usually grams) of a substance one degree celsius. High specific heat = hard to change their temperature, Low specific heat = easy to change their temperature
In these kind of energy exchange problems where you have a metal in water you have a functionally closed system (that is why they indicate it is in a calorimeter), meaning no heat is "lost" to the environment. For these problems you can use the following equation for heat transfer:
Q = mcΔT where Q is heat transfer, m is mass, c is specific heat and ΔT is the change in temperature
1) We can set the equation up for water: Qw = mcΔT and then for the Qm = mcΔT
2) We know these things come to a final equilibrium in a closed system, meaning that all heat transfer from the metal will be absorbed by the water. For example, if the heat transfer to water was +20 (water gained heat energy), then by definition the metal heat transfer would have to be -20 (because the only source of that energy was the metal, so that has to be the amount of energy the metal lost). This is a longer way of basically saying we can set Qw = -Qm You can then replace the Q's with their respective mcΔT equations.
3) Now it is just a plug-and-chug solve for the variable (the specific heat of the metal) question. Because we know the final temperature they both reach, we can plug in the specific heat of water, the mass of the water, and the amount of temperature change of the water as well as the mass and temperature change of the unknown metal. Put all the numbers in and solve for the c of the metal. Just remember to make sure your units are correct!
I hope this helped!
