Question

To measure the heat capacity of an object, all you usually have to do is put it in thermal contact with another object whose heat capacity you know. As an example, suppose that a chunk of metal is immersed in boiling water (100°C), then is quickly transferred into a Styrofoam cup containing 250 g of water at 20°C. After a minute or so, the temperature of the contents of the cup is 24°C. Assume that during this time no significant energy is transferred between the contents of the cup and the surroundings. The heat capacity of the cup itself is negligible.

(a) How much heat is lost by the water?
(b) How much heat is gained by the metal?
(c) What is the heat capacity of this chunk of metal?
(d) If the mass of the chunk of metal is 100 g, what is its specific heat capacity?

Answer 1

To measure the heat capacity of an object, you can use a process called calorimetry. In this example, a metal is immersed in boiling water and then transferred to a Styrofoam cup containing cooler water. By measuring the changes in temperature, you can determine the heat lost by the water and the heat gained by the metal. The specific heat capacity of the metal can then be calculated by dividing its heat capacity by its mass.

Step-by-step explanation:

In order to measure the heat capacity of an object, you can use a process called calorimetry. In the given example, a chunk of metal is immersed in boiling water and then transferred into a Styrofoam cup containing water at a lower temperature. By observing the change in temperature of the water in the cup, you can determine the heat lost by the water and the heat gained by the metal.

(a) To calculate the heat lost by the water, you can use the formula Q = mcΔT, where Q is the heat lost, m is the mass of the water, c is the specific heat capacity of water, and ΔT is the change in temperature.

(b) To calculate the heat gained by the metal, you can use the same formula Q = mcΔT, but this time m is the mass of the metal and c is the specific heat capacity of the metal.

(c) The heat capacity of the metal is given by the formula C = Q/ΔT, where C is the heat capacity, Q is the heat gained by the metal, and ΔT is the change in temperature.

(d) The specific heat capacity of the metal can be calculated by dividing its heat capacity by its mass, using the formula c = C/m.