Question

if you transfer heat energy to a perfectly insulated cup of some liquid (no heat energy can be transferred in or out through the walls) what determines how much the temperature changes? Does it depend on how much heat energy you transfer, how much liquid there is in the cup, what the liquid is, or what the initial temerpature of the liquid is? Which of these factors do you think make a differnce in how much the temperture rises?

Answer 1

Suppose we are able to successfully transfer heat to the cup. We expect a change in temperature as a result of heat transfer. The amount of heat required to cause a change in temperature is proportional to the mass of the object as well as the change in the temperature of the object.

For example, if we want to increase the temperature of 2kg object we need to supply twice as much heat as we need to cause the same change in temperature of 1kg object. Or you can imagine increasing the temperature of two 1kg objects separately, and combining them after increasing the temperature of each object. In either way, the heat require will be twice for 2kg.

Also if we want to change the temperature of an object by 10°C we expect to supply twice the heat we would supply to change temperature by 5°C. Suppose you are increasing temperature of water from 30°C to 40°C. The heat required to increase temperature from 30°C to 35°C is equal to that required to increase from 35°C to 40°C.

The proportionality constant is called the specific heat capacity, it depends upon the substance. It is measure of how easy it is to change the temperature of a substance. For water C=4.186J/g/°C, that is, 4.186 Joules of heat energy is required to change the temperature of 1 gram water by 1°C. For mercury C=0.140J/g/°C. So the change in temprature will depend on the liquid.

The initial temperature has no important role, only important quantity is the change in temperature. We can write the equation as