Thermodynamics — MEEN 315

Energy Balance for a Closed System.

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For closed systems, the only possible exchange of energy across the system boundary is by heat transfer and by work. Our convention is to write work done by the system as positive, and heat transfer to the system as positive. As such, for any process, we may relate heat transfer and work to the change in kinetic, gravitational, and internal potential energies within the system.

$$ Q-W=\Delta U_k+\Delta U_g+\Delta U_i=\frac 12m\Delta(v^2)+m\Delta z+m\Delta u $$

Work

When work is done by a force, it may be calculated by the line integral of a force. That force in turn may be calculated as the surface integral of a pressure. In many introductory thermodynamic problems this pressure will be constant across the surface and the line integral, in which case we pay calculate work as the product of pressure and the volume change.

$$ W=\int F~ds=\int\begin{pmatrix} \int p~dA \end{pmatrix}ds\approx p~\Delta $$

However, work is a very general concept, and may include work wone by electricity, or by many other means, necessitating other methods of calculation.

Heat Transfer

Heat transfer can occur by conduction, convection, or radiation. Conduction is heat transfer by contact. Convection is heat transfer to a moving fluid, such as to ambient air. Radiation is heat transfer by emission of electromagnetic waves. You won’t often be concerned with calculating these quantities in thermodynamics at A&M, because that is the focus of Heat Transfer — MEEN 461.

$$ \begin{matrix} \dot{Q}{conduction}=-\kappa A\frac{dT}{dx}& \dot{Q}{radiation}=\varepsilon\sigma A_s(T_s^4-T_{surr}^4)& \dot{Q}{convection}=hA_s(T_s-T\infin) \end{matrix} $$