Mathematical relationship between heat specific capacity mass and temperature change

Specific Heat Formula

mathematical relationship between heat specific capacity mass and temperature change

Heat capacity is the heat to increase the 1°C temp. Of substance. Wherever, Specific heat capacity is the heat to increase the 1°C temp. Of unit mass of. Relationship between heat and temperature Heat capacity: Converting between heat and change in temperature . Note that both mass and specific heat capacity can only have positive values, so the sign of q \text q q will Math · Math by grade · Science & engineering · Computing · Arts & humanities · Economics &. Calculate the change in temperature of a substance given its heat capacity and often simply called specific heat, which is the heat capacity per unit mass of a .. relationship is represented by the specific heat capacity of the substance, C.

Defining thermal equilibrium The zeroth law of thermodynamics defines thermal equilibrium within an isolated system.

BBC - Intermediate 2 Bitesize Physics - Heat : Revision

The zeroth law says when two objects at thermal equilibrium are in contact, there is no net heat transfer between the objects; therefore, they are the same temperature. Another way to state the zeroth law is to say that if two objects are both separately in thermal equilibrium with a third object, then they are in thermal equilibrium with each other. The zeroth law allows us to measure the temperature of objects.

Any time we use a thermometer, we are using the zeroth law of thermodynamics. Let's say we are measuring the temperature of a water bath. In order to make sure the reading is accurate, we usually want to wait for the temperature reading to stay constant.

We are waiting for the thermometer and the water to reach thermal equilibrium! At thermal equilibrium, the temperature of the thermometer bulb and the water bath will be the same, and there should be no net heat transfer from one object to the other assuming no other loss of heat to the surroundings.

Heat and Temperature

Converting between heat and change in temperature How can we measure heat? Here are some things we know about heat so far: When a system absorbs or loses heat, the average kinetic energy of the molecules will change. Thus, heat transfer results in a change in the system's temperature as long as the system is not undergoing a phase change. This is because the specific heat capacity of aluminum is nearly twice the value of iron.

  • Specific heat capacity and calculating heat energy
  • Heat and temperature
  • Specific Heat Formula

Heat capacities are listed on a per gram or per kilogram basis. Occasionally, the value is listed on a per mole basis, in which case it is called the molar heat capacity.

mathematical relationship between heat specific capacity mass and temperature change

The fact that they are listed on a per amount basis is an indication that the quantity of heat required to raise the temperature of a substance depends on how much substance there is. Any person who has boiled a pot of water on a stove, undoubtedly know this truth. This temperature change is achieved by the absorption of heat from the stove burner. One quickly notices that it takes considerably more time to bring a full pot of water to a boil than to bring a half-full of water to a boil.

This is because the full pot of water must absorb more heat to result in the same temperature change. In fact, it requires twice as much heat to cause the same temperature change in twice the mass of water.

The fact that the specific heat capacity is listed on a per degree basis is an indication that the quantity of heat required to raise a given mass of substance to a specific temperature depends upon the change in temperature required to reach that final temperature. In other words, it is not the final temperature that is of importance, it is the overall temperature change. A person who wishes to bring water to a boil on a stovetop more quickly should begin with warm tap water instead of cold tap water.

mathematical relationship between heat specific capacity mass and temperature change

This discussion of specific heat capacity deserves one final comment. The term specific heat capacity is somewhat of a misnomer. The term implies that substances may have the ability to contain a thing called heat. As has been previously discussed, heat is not something that is contained in an object. Heat is something that is transferred to or from an object. Objects contain energy in a variety of forms. When that energy is transferred to other objects of different temperatures, we refer to transferred energy as heat or thermal energy.

While it's not likely to catch on, a more appropriate term would be specific energy capacity. Relating the Quantity of Heat to the Temperature Change Specific heat capacities provide a means of mathematically relating the amount of thermal energy gained or lost by a sample of any substance to the sample's mass and its resulting temperature change. The relationship between these four quantities is often expressed by the following equation.

Measuring the Quantity of Heat

When using the above equation, the Q value can turn out to be either positive or negative. As always, a positive and a negative result from a calculation has physical significance.

Knowing any three of these four quantities allows an individual to calculate the fourth quantity. A common task in many physics classes involves solving problems associated with the relationships between these four quantities. As examples, consider the two problems below. The solution to each problem is worked out for you.