derive expression for heat exchanged in an isochoric process
Answers
The heat transferred to the system does work but also changes the internal energy of the system. Explanation: In an isobaric process for a monatomic gas , heat and temperature change satisfy the following equation : Q=5 2 N K ( TRIANGLE)
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Explanation:
The isochoric process is one of several idealized thermodynamic processes which describe how the states of an ideal gas can undergo change. It describes the behavior of gas in a closed container at a constant volume. In this situation, when energy is added, only the temperature of the gas changes; it does no work on its surroundings. So no motors turns, no pistons move, and no useful output happens.
What Is an Isochoric Process?
An isochoric process, (sometimes called isovolumetric or isometric process) is a thermodynamic process that occurs at a constant volume. Because the volume doesn't change, the relationship between pressure and temperature maintains a constant value.
This can be understood by starting with the ideal gas law:
PV = nRT
Where P is the absolute pressure of the gas, V is volume, n is the amount of gas, R is the ideal gas constant (8.31 J/mol K), and T is temperature.
When volume is held constant, this law can be rearranged to show that the ratio of P to T must also be a constant:
\frac {P}{T} = \text {constant}
T
P
=constant
This mathematical expression of the ratio between pressure and temperature is known as Gay-Lussac's Law, so named for the French chemist who came up with it in the early 1800s. Another outcome of this law, which is sometimes also called the pressure law, is the ability to predict temperatures and pressures for ideal gasses undergoing isochoric processes using the following equation:
\frac {P_1}{T_1} = \frac {P_2}{T_2}
T
1
P
1
=
T
2
P
2
Where P1 and T1 are the initial pressure and temperature of the gas, and P2 and T2 are the final values.
On a graph of pressure versus temperature, or a PV diagram, an isochoric process is represented by a vertical line.
Teflon (PTFE), the non-reactive, most slippery substance on the planet with applications across many industries from aerospace to cooking, was an accidental discovery that resulted from an isochoric process. In 1938, DuPont chemist Roy Plunkett had set up a bunch of small cylinders to store tetrafluoroethylene gas, for use in refrigeration technologies, which he then cooled to an extremely low temperature.
When Plunkett went to open one later, no gas came out, though the mass of the cylinder hadn't changed. He chopped open the tube to investigate and saw a white powder coating the inside, which later proved to have immensely useful commercial properties.
According to Gay-Lussac's Law, when the temperature rapidly decreased, so did the pressure to initiate a phase change in the gas.
Isochoric Processes and The First Law of Thermodynamics
The first law of thermodynamics states that the change in the internal energy of a system is equal to the heat added to the system minus the work done by the system. (In other words, energy input minus energy output.)
The work done by an ideal gas is defined as its pressure times its change in volume, or PΔV (or PdV). Because the volume change ΔV, is zero in an isochoric process, however, no work is done by the gas.
Hence, the change in internal energy of the gas is simply equal to the amount of heat added.
An example of a nearly isochoric process is a pressure cooker. When sealed closed, the volume inside cannot change, so when heat is added both pressure and temperature increase rapidly. In actuality, pressure cookers do expand slightly, and some gas is released from a valve on top.