See also: What is an Ideal Gas
Let assume an isochoric heat addition in an ideal gas. In an ideal gas, molecules have no volume and do not interact. According to the ideal gas law, pressure varies linearly with temperature and quantity, and inversely with volume.
pV = nRT
- p is the absolute pressure of the gas
- n is the amount of substance
- T is the absolute temperature
- V is the volume
- R is the ideal, or universal, gas constant, equal to the product of the Boltzmann constant and the Avogadro constant,
In this equation the symbol R is a constant called the universal gas constant that has the same value for all gases—namely, R = 8.31 J/mol K.
The isochoric process can be expressed with the ideal gas law as:
On a p-V diagram, the process occurs along a horizontal line that has the equation V = constant.
Pressure-volume work by the closed system is defined as:
Since the process is isochoric, dV = 0, the pressure-volume work is equal to zero. According to the ideal gas model, the internal energy can be calculated by:
∆U = m cv ∆T
where the property cv (J/mol K) is referred to as specific heat (or heat capacity) at a constant volume because under certain special conditions (constant volume) it relates the temperature change of a system to the amount of energy added by heat transfer.
Since there is no work done by or on the system, the first law of thermodynamics dictates ∆U = ∆Q. Therefore:
Q = m cv ∆T
See also: Specific Heat at Constant Volume and Constant Pressure
See also: Mayer’s formula