THD - Temperature and Heat

Temperature and Heat

Introduction

From chemistry you know that a measurement of an object's temperature is a measure of the average kinetic energy of the molecules in the object. The higher the temperature, the greater the average kinetic energy of the molecules, and the hotter we say an object is. In this course we measure temperature using SI units of Kelvin (K). A unit of 1K = 1°C. A temperature of 0K = -273.15 °C. To convert, .

When you pick up a pot by its metal handle from the stove and find it to be hot, you're sensing the transfer of thermal energy from the hot pot to your relatively cool hand. Likewise, the sensation that an ice cube feels cold comes from the transferring of thermal energy from your hand to the lower temperature ice cube. The molecules of two objects in thermal contact will transfer thermal energy in order to reach a state of thermal equilibrium (when two objects are at the same temperature).

Thermal Expansion

What does this mean for objects in two or three dimensions?

Consider a closed loop of metal. How will the expansion of this metal loop, when heated, affect the diameter of the inner hole?

Make a prediction: Will the metal expand inward and decrease the diameter of the hole? or Will the expanding loop cause the diameter of the hole to increase?

Think through the process.  You should be able to determine that if a straight rod is heated that it will get longer.  Now if we bend a rod into a ring and heat the ring, the same change would occur.  As the rod gets longer the ring would get bigger and the hole would also get larger.  You can see a demonstration of thermal expansion in the video below.

Heat

Heat is the energy transferred from one object to another because of a difference in temperature. Because it measures energy, heat is measured in SI units of joules (J).

We need to make a distinction between three quantities: temperature, heat, and internal energy.

• Temperature is a measure of the average kinetic energy of an object's individual molecules.
• Internal energy is the total energy of all molecules in an object.
• Heat is the transfer of energy between two objects that have different temperatures.

Calculating the average kinetic energy of an object's molecules looks like . The internal energy, U, would, therefore, be , where again N, is the total number of molecules. Combining these equations with our definition of temperature and the ideal gas law gives us:  

This useful equation shows us that the total internal energy of an ideal, monatomic gas is related only to how much gas is present and the temperature of that gas.

Specific Heat

When heat flows into or out of an object, its temperature will change. But by how much? The answer to that question is determined by the object's specific heat. The equation for the calculation looks like: where Q = heat, m = mass, c = specific heat.

The higher the specific heat for a substance, the more heat it can absorb without appreciably increasing the temperature of the substance. A substance like liquid water, with c = 4186 J/kg•C° acts more like an insulator than a substance like copper, with c = 390 J/kg•C°. We say copper is a good thermal conductor.

Specific Heat Practice

A. How much heat input is needed to raise the temperature of a an empty 20-kg vat made of iron from 10°C to 90°C? (c of iron = 450 J/kg•C°) B. What if the vat is filled with 20 kg of water? 

Click here for practice problem solution. Links to an external site.

To measure the specific heat of a substance, scientists use a device called a calorimeter. To use a calorimeter, the unknown substance is heated to a known temperature then placed in an insulated, water-filled chamber. The equilibrium temperature of the water/substance is taken and used to find the change in temperature for both the water and unknown substance. Since the thermal energy lost from the unknown substance must equal the energy gained by the water we set up our specific heat equation

 

Heat Transfer

Heat transfer occurs through one of three, primary methods: conduction, convection, and radiation. Conduction occurs when heat is transferred through contact. High temperature/speed molecules in the hot object essentially collide with low temperature/speed molecules in the cold object transferring some of their kinetic energy. The rate at which thermal energy will transfer via conduction depends on several factors: the size of the contact area, the difference in temperature between the objects, and the thermal conductivity of the material. The rate of heat flow (Q/t) can be calculated by   where k = thermal conductivity (will usually be given), A = cross-sectional area of contact, and l = distance energy must travel to get from the hot object to the cool object. From this we can see that the greater the thermal conductivity, the greater the area, or the greater the difference in temperature, the quicker the heat will flow.

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