Technical work

The Technical Working is a term used in thermodynamics . It is about the shaft work in an open system , which is transmitted via the shaft of a heat engine or a work machine. ${\displaystyle W_{\mathrm {t} }}$

The definition differs in the relevant literature. Often only the reversible part is defined as technical work (see below) and the work, which also contains the dissipated energy , is referred to as "inner work". ${\displaystyle \int Vdp+\Delta E_{\mathrm {a} }}$ ${\displaystyle W_{\mathrm {diss} }}$

Relation to the volume change work

Relationship between volume change work and technical work in the pV diagram

While the volume change work is a one-time work performed on the closed system , the technical work is transferred continuously or periodically . In addition to the volume change work, there is also the shift work at the entry and exit of the system:

${\displaystyle \mathrm {\delta } W_{\mathrm {t} }=Vdp+\delta W_{\mathrm {diss} }+\delta E_{\mathrm {a} }}$( infinitesimal consideration)

or.

${\displaystyle {\begin{aligned}W_{\mathrm {t} }&=\int _{1}^{2}V\ dp+W_{\mathrm {diss} }+\Delta E_{\mathrm {a} }\\&=W_{\mathrm {vol} }+W_{\mathrm {diss} }+W_{\mathrm {versch} }\\&=\underbrace {-\underbrace {\int _{1}^{2}p\ dV} _{<0}} _{>0}+W_{\mathrm {diss} }+p_{2}V_{2}-p_{1}V_{1}\end{aligned}}}$

Here the change in the external energies, i.e. H. the change in the sum of kinetic and potential energy , cf. Energy balance for any open system . ${\displaystyle \Delta E_{\mathrm {a} }}$

In relation to time , one obtains the relationship for the performance :

${\displaystyle P=\int _{1}^{2}{\dot {V}}dp+{\dot {W}}_{\mathrm {diss} }+\Delta {\dot {E}}_{\mathrm {a} }}$

or with the mass flow and the specific quantities :

${\displaystyle P={\dot {m}}\cdot \left(\int _{1}^{2}\ vdp+\ w_{\mathrm {diss} }+\Delta \ e_{\mathrm {a} }\right)}$

Illustration using the example of a piston compressor

Illustration using the example of a piston compressor

The composition of the technical work from volume change work and shift work can be illustrated well using a piston compressor , the piston of which is moved by a crank drive (only indicated by a rod in the sketch):

• The pushing work is transferred from the pressure accumulator  1 with the pressure to the piston of the compressor. Then the chamber volume is the same at bottom dead center (in the sketch on the right) . ${\displaystyle p_{1}V_{1}}$ ${\displaystyle p_{1}}$ ${\displaystyle V_{1}}$
• Volume change work: by moving the piston from bottom dead center to the left, the pressure of the gas is increased and its volume is reduced when the valves are closed (point 1 to point 2 of the above diagram). The valves can be thought of as flaps that close automatically due to excess pressure on the plate side and vice versa. When moving to the left, the lower flap closes; the upper one only opens when the pressure has been reached through compression ( volume work in a closed system) . ${\displaystyle p_{2}}$
• After performing the volume change work, the compressor has to perform the pushing out work in order to push the gas into the cylinder  2 at a constant pressure . When moving to top dead center (to the left in the sketch), the piston ideally pushes the gas out completely, i.e. H. the chamber volume is then zero. ${\displaystyle p_{2}V_{2}}$ ${\displaystyle p_{2}}$

The sum of the work done is the technical work that must be done by the crankshaft . The process is repeated with the next turn of the crank.

See also: Gas exchange in a gasoline engine

Web links

• University of Duisburg-Essen, basics of technical thermodynamics with exercises and solutions

Individual evidence

1. ↑ ^{a b c} Volker Sperlich: "Exercises on Thermodynamics with Mathcad" (2002) Fachbuchverlag Leipzig
2. ↑ Fundamentals of technical thermodynamics