A 22.5-g piece of unknown metal is heated to 100*C then transferred quickly and without cooling into 100mL of water at 20.0*C. The final temperature reached by

Question

26.9*c calculate the specific heat of the metal in J/g*C. Show all work. 

how do you solve this? What do you plug in into an equation

 

Answer 1

Dear Xochitl,

This is a typical heat transfer problem. The metal cools down from its initial temperature to the final temperature; the water heats up from its initial temperature to the final temperature. For each of these temperature changes in a material, the heat gain is Q = mass * temperature_change * specific_heat (of that material). [Note: there were no phase changes to also add in.] Set these two equations up. You may need to look up the specific_heat of water (I always remember it as exactly 1 cal g^-1 K^-1 and convert to J = 4.184 J g^-1 K^-1 ).

Temperature change is defined as T(final) - T(initial). Watch your signs; a lower temperature => negative ΔT.

You have one unknown, in the equation for the metal, and you know that the heat loss by the metal = the heat gain by the water [you have to flip the sign!](one heat change is negative, that's a loss, and one is positive, that's a gain).

That should get you through.

By the way, you could also use the Dulong-Petit law to find out which metal it is: heat capacity is 24.94 J K^-1 mol^-1 for metals in general. You should be able to calculate the number of moles of metal you had, and from that and the mass, the atomic weight => identity.