Isochoric Process Definition and Use

An isochoric process is a thermodynamic process in which the volume remains constant. Since the volume is constant, the system does no work and W 0. (W is the abbreviation for work.) This is perhaps the easiest of the thermodynamic variables to control since it can be obtained by placing the system in a sealed container which neither expands nor contracts. First Law of Thermodynamics To understand the isochoric process, you need to understand the first law of thermodynamics, which states: The change in a systems internal energy is equal to the difference between heat added to the system from its surroundings and work done by the system on its surroundings. Applying the first law of thermodynamics to this situation, you find that: delta-Since delta-U is the change in internal energy and Q is the heat transfer into or out of the system, you see that all of the heat either comes from internal energy or goes into increasing the internal energy. Constant Volume It is possible to do work on a system without changing the volume, as in the case of stirring a liquid. Some sources use isochoric in these cases to mean zero-work regardless of whether there is a change in volume or not. In most straightforward applications, however, this nuance will not need to be considered—if the volume remains constant throughout the process, it is an isochoric process. Example Calculation The website  Nuclear Power, a free, nonprofit online site built and maintained by engineers, gives an example of a calculation involving the isochoric process. 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. The basic formula would be: pV nRT where: p  is the absolute pressure of the gasn  is the amount of substanceT  is the absolute temperatureV  is the volumeR  Ã‚  is the ideal, or universal, gas constant equal to the product of the Boltzmann constant  and the Avogadro constantK is the scientific abbreviation for  Kelvin 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  Joule/mole  K. The isochoric process can be expressed with the ideal gas law as: p/T constant 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  Ã¢Ë†â€ T where the property  cv  (J/mole 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  Ã¢Ë†â€ U ∆Q.  Therefore: Q   m cv  Ã¢Ë†â€ T