Temperature and Heat

TEMPERATURE AND HEAT

TEMPERATURE

There are numerous measurable physical properties that vary as temperature varies. these can be:

·       Liquid volume

·       The length of a rod

·       A wire’s electrical resistance

·       The pressure of a gas kept at constant volume

·       The volume of a gas kept at constant pressure.

 

Isothermal Process

This is a process that occurs at a constant temperature. It is important to note that if the initial and final states are at the same temperature, it does not necessarily imply that it’s an isothermal process.

Exercise: Which of the following processes are isothermal?

a)     A tank of compressed air at room temperature leaks air through a tiny leak.

b)     A large valve in the tank above is opened allowing the pressure to fall to atmospheric pressure.

c)     Heat is added to water boiling on a stove.

d)     The pressure of air in a piston-cylinder device is quickly increased from 1 bar to 15 bar.

 

Solution: Processes (a) and (c) are isothermal. In process (a), the rate of gas escape is so slow that time is ample for heat transfer to keep the temperature constant. Processes (b) and (d) are not isothermal because they are too rapid for the significant heat transfer required to keep the temperature constant.

HEAT

Heat is the transfer of thermal energy from one system to another due to a temperature difference between the two i.e., heat flows flow a higher to lower temperature. For any given substance the amount of thermal energy is measured by temperature. Temperature is a measure of the average kinetic energy of individual molecules. Thermal (or internal) energy, refers to the total energy of all the molecules in the object. The higher the temperature, the more thermal energy is present. However, an increase in thermal energy need not raise the temperature if there is a change of phase, as in the boiling water.

According to the sign convention for heat, if the system receives heat from the surroundings, it is positive. Otherwise, it is negative.

Heat Capacity

The amount of heat, Q, required to change the temperature of the system is found to be proportional to the mass, m, of the system and to the temperature change, ΔT. This implies

where the proportionality constant K is defined as:

Therefore, Q can be defined as follows:

Ĉ_v (or, Ĉ_p) can be viewed as the energy required to raise the temperature of the unit mass of a substance by one degree as the volume (or, pressure) is maintained constant. A common unit for heat capacity is kJ/kg.K or kJ/kg.°C. For solids and liquids Ĉ_v ≈ Ĉ_p.

For gases, however, Ĉ_p is always greater than Ĉ_v because at constant pressure the system is allowed to expand and the energy for this expansion work must also be supplied to the system. For monatomic and diatomic gases, Ĉ_v and Ĉ_p values are given as:

The above relationships can be expressed in the following way for an ideal gas:

Heat capacities of gases are only moderate functions of temperatures and thus for ordinary changes in temperature, i.e., up to several hundreds of degrees for air, the use of constant heat capacities is valid for engineering purposes. If heat capacities are dependent on temperature, then they are expressed as follows:

Specific Heat

This is the ratio of the amount of heat necessary to cause unit change in temperature of a unit mass of the material in question to the amount of heat necessary to raise an equal mass of water one unit on the temperature scale, both processes being carried out along paths subject to the same restrictions, i.e., either at constant pressure or constant volume.

Note that specific heats are dimensionless quantities, whereas heat capacities have the dimensions of energy/(mass) (degree of temperature).

 

Adiabatic Process

This is a process that has no heat transfer between the system and its surroundings. There are two ways a process can be adiabatic:

·       A well-insulated system so that only negligible heat can pass through the boundary.

·       Both the system and its surroundings are at the same temperature, thus no driving force i.e., temperature difference, for heat transfer.

An adiabatic process should not be confused with an isothermal process. Although there is no heat transfer during an adiabatic process, the temperature of a system can be changed by other means such as work.

In determining whether a given process is adiabatic or isothermal, note the following characteristics of these two processes:

·       Heat transfer is a slow process and hence usually negligible in processes that take place very rapidly. There is no way to be absolute in this statement because slow and rapid are relative terms. Nevertheless, processes that occur in a matter of seconds can usually be assumed to be adiabatic.

·       Processes that occur slowly allow time for heat transfer and are usually assumed to be isothermal. The adiabatic and isothermal processes are often opposite extremes. In reality, processes fall in between.