Engineering and fabrication

How do you find specific heat of a metal without knowing the thermal energy?

A piece of metal weighing 500.0 g is put into a boiling water bath. After 10 minutes, the metal is immediately placed in 250.0 g of water at 40.0 °C. The maximum temperature that the system reaches is 50.0 °C. What is the specific heat of the metal?

Public Comments

1. use:

   MCdeltaTwater = -MCdeltaT metal

   M=500

   C=?

   deltaT=25 (assuming it starts at rm temp which is 25)

   M=250

   C=4.18

   deltaT=10

   now solve by 250*4.18*10/12500



2. For the water to go from 40 C to 50 C with a mass of 250 grams takes 2500 calories.

   250 gm* (50c-40c) = 2500 calories

   The specific heat equation is :

   Heat added = specific heat * mass *(T final - T initial)

   Plug in the values.

   Metal Mass = 500 grams

   amount of heat added = 2500 calories

   initial temperature = 40C

   final temperature = 50C

   (went backwards here but same temp differential)

   Solve for specific heat and you get

   Specific heat = 0.5 cal/gm C or 2.0934 joule/gm C

   depending on units used.

   The boiling water makes no difference in this problem. The boiling water was simply a uniform heat source that could be weighed and measured easily. The important thing was the metal warmed the water from 40c to 50c. The metal at maximum temperature reached 100C and the heat of that metal is what warmed up by the 250gm of water by 10C