Question

State the first law of thermodynamics for isochoric processes.

Answer 1

Thermodynamics is a field of physics that studies heat, work, and temperature, as well as their relationships with energy, radiation, and matter's physical characteristics. The four principles of thermodynamics control the behaviour of these quantities, which provide a quantitative description using quantifiable macroscopic physical characteristics but may be described by statistical mechanics in terms of microscopic components.

Complete step-by-step solution:
The isochoric process is a thermodynamic process that occurs at a fixed volume. It's also known as an isometric process or a constant-volume process. Isochoric is derived from the Greek terms iso, which means constant, and choric, which indicates space or volume. A process that is isochoric is one in which. ${V_f}\; = {\text{ }}{V_i}\;\left( {\Delta v{\text{ }} = {\text{ }}0,{\text{ }}dv{\text{ }} = {\text{ }}0} \right)$
Heat is a type of energy, according to the First Law of Thermodynamics, and thermodynamic processes are thus subject to the concept of energy conservation. Heat energy cannot be generated or destroyed in this way. It can, however, be moved from one area to another and transformed into and out of other types of energy.
$\Delta U{\text{ }} = {\text{ }}q{\text{ }} + {\text{ }}W$
In an isochoric process, no work is done. As a result of the first rule of thermodynamics,
$P{\text{ }} = {\text{ }}dW$When V is constant,$dV{\text{ }} = {\text{ }}0$.
$dQ{\text{ }} = {\text{ }}dU$ (isochoric process).
The rise or reduction in the system's internal energy is also equal to the total heat supplied or rejected.

Note: An isochoric process, also known as a constant-volume process, isovolumetric process, or isometric process, is a thermodynamic process in which the volume of the closed system undergoing the process remains constant during the process. The heating or cooling of the contents of a sealed, inelastic container is an example of an isochoric process: The thermodynamic process is the addition or removal of heat; the closed system is established by the isolation of the container's contents; and the container's inability to deform imposes the constant-volume constraint. The isochoric process in this case should be quasi-static.