A thermodynamic system is taken from state a to state c in...

A thermodynamic system is taken from state $a$ to state $c$ in Fig. 19.29 along either path $a b c$ or path $a d c .$ Along path $a b c$ , the work $W$ done by the system is 450 . Along path adc, $W$ is 120 J. The internal energies of each of the four states shown in the figure are $U_{a}=150 \mathrm{J}$ , $U_{b}=240 \mathrm{J}, U_{c}=680 \mathrm{J},$ and $U_{d}=330 \mathrm{J}$ . Calculate the heat flow $\mathrm{w}$ $Q$ for each of the four processes $a b, b c, a d,$ and $d c$ . In each process, does the system absorb or liberate heat?

Key Concepts

Heat Flow Calculation

Calculating the heat flow in any process involves manipulating the first law of thermodynamics. By rearranging the equation ?U = Q - W, one can determine the heat transfer as Q = ?U + W for each process. This calculation is fundamental for quantifying the energy exchange in thermodynamic processes and determining whether the system is absorbing heat or releasing it.

Sign Conventions in Thermodynamics

Proper use of sign conventions is critical when analyzing thermodynamic processes. Typically, work done by the system is considered positive, while work done on the system is negative; similarly, heat added to the system (absorbed) is taken as positive and heat released as negative. These conventions help in consistently applying the first law of thermodynamics and correctly interpreting the nature of energy exchanges in any process.

Path Dependence in Thermodynamic Processes

The quantities of work and heat are path-dependent, meaning that they can vary even when a system starts and ends at the same state. This concept is important in thermodynamics because it explains how different procedures (or paths) to change a system's state can lead to significantly different energy exchanges, even though the change in a state function such as internal energy remains constant.

First Law of Thermodynamics

This principle states that the change in a system's internal energy is equal to the heat added to the system minus the work done by the system. It is a statement of energy conservation applied to thermodynamic processes. Understanding this law is crucial because it relates the internal energy, heat transfer, and work in any process, irrespective of the specific pathway taken by the system.

State Functions vs Path Functions

State functions, such as internal energy, depend only on the current state of a system and not on the path taken to reach that state. In contrast, path functions like heat and work depend on the specific process or path followed between two states. Recognizing this distinction is essential for analyzing thermodynamic processes and understanding why different paths between the same states can yield different heat and work values.

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