- #1
sparkle123
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I know ΔA=ΔU-TΔS
how does this lead to ΔA=-integral(PdV)? (which seems like work)
how does this lead to ΔA=-integral(PdV)? (which seems like work)
The derivation of dA=-PdV is a mathematical process used in thermodynamics to calculate the change in internal energy of a system. It is based on the first law of thermodynamics, which states that the change in internal energy of a system is equal to the heat added to the system minus the work done by the system.
In the derivation of dA=-PdV, the negative sign is included to represent the direction of work. When a gas expands, it does work on the surroundings and the volume increases (dV is positive). This work done by the gas is equivalent to the decrease in internal energy (dA is negative). Therefore, dA=-PdV represents the relationship between the change in internal energy and the work done by a system.
"d" in the equation dA=-PdV represents an infinitesimal change. In other words, it is a very small change that is close to zero but not zero. It is used in calculus to denote a small change in a variable.
dA represents the change in internal energy of a system, while dV represents the change in volume. These two variables are related through the work done by the system, as shown in the equation dA=-PdV. This relationship is important in understanding the behavior of thermodynamic systems and calculating their internal energy.
The derivation of dA=-PdV is used in various fields, such as engineering, chemistry, and physics, to analyze and predict the behavior of thermodynamic systems. It can be applied to understand the efficiency of engines, the expansion of gases, and the behavior of chemical reactions. It is also used in the design and optimization of industrial processes and equipment.