# Homework Help: Specific Heat Capacity Problem.(Please check.)

1. May 3, 2006

### shulien

This is CALORIMETRY PROBLEM.

A 0.050kg metal bolt is heated to an unknown initial temperature. It is then dropped into a beaker containing 0.15kg of water with an initial temperature of 21.0 C. The bolt and metal then reach a final temperature of 25.0 C. If the metal has a specific heat capacity of 899 J/kg*C, find the initial temperature of the metal.

the solution is:

Change in Temp of metal = (C of water *mass of water* Change in temp of water)/(C of metal*mass of metal)

Change of temp. of metal = [(4186 J/kg*C)(0.15kg)(25C-21C)]/[(899 j/kg*C)(0.050kg)
Change of temp. of metal = 55.87C

Change in temperature = Final Temperature-Initial Temperature
Initial Temperature = Final Temp.-Change in Temp
=25C-55.87C
= -30.87C

i hope you could explain so i can also explain it to my students. is the sign of the answer has something to do with the HEAT REMOVAL and HEAT ABSORPTION?

Thanks!

Last edited: May 3, 2006
2. May 3, 2006

### Staff: Mentor

This is off by a minus sign. The net change in thermal energy of "metal + water" is zero, so:
Change in Temp of metal = - (C of water *mass of water* Change in temp of water)/(C of metal*mass of metal)

The change in temp of the metal is -55.87C, not +. (The metal cools down.)

25C - (-55.87C) = +80.87C
Just keep in mind that the "heat" gained by the water must equal the "heat" removed from the metal. In terms of Q: For the water, Q = + (it heats up); for the metal, Q = - (it cools down). The net Q is zero.

3. May 3, 2006