1 Arbeit und Energie

• \begin {equation*} W = m\cdot g \cdot h \end {equation*} \begin {equation*} W = 10 kg \cdot 9,81 \frac {m}{s^2}\cdot 5 m \end {equation*} \begin {equation*} W = 490,5J \end {equation*}
• \begin {equation*} Wirkungsgrad = \frac {genutzte Energie}{aufgewendete Energie} = \eta \end {equation*} \begin {equation*} E_{zu}=\frac {W}{\eta }=\frac {490,5J}{80\%}=613,125J \end {equation*}

2 Höhenenergie im Stausee

• \begin {equation*} E_{\text {pot}} = m \cdot g \cdot h \end {equation*} \begin {equation*} m = \rho \cdot V = 1000\,\mathrm {kg/m^3} \times 2\,000\,000\,\mathrm {m^3} = 2\,000\,000\,000\,\mathrm {kg} \end {equation*} \begin {equation*} E_{\text {pot}} = 2\,000\,000\,000\,\mathrm {kg} \times 9{,}81\,\mathrm {m/s^2} \times 100\,\mathrm {m} \end {equation*} \begin {equation*} E_{\text {pot}} = 1{,}962 \times 10^{12}\,\mathrm {J} \end {equation*}

3 Bewegungsenergie eines Autos

• \begin {equation*} E_{\text {kin}} = \frac {1}{2} m v^2 \end {equation*} \begin {equation*} m = 1200\,\mathrm {kg} \end {equation*} \begin {equation*} v = 72\,\mathrm {km/h} = 72 \times \frac {1000\,\mathrm {m}}{3600\,\mathrm {s}} = 20\,\mathrm {m/s} \end {equation*} \begin {equation*} E_{\text {kin}} = \frac {1}{2} \times 1200\,\mathrm {kg} \times (20\,\mathrm {m/s})^2 \end {equation*} \begin {equation*} E_{\text {kin}} = 240\,000\,\mathrm {J} \end {equation*}

4 Elektrische Energie eines Geräts

• \begin {equation*} P = 2000\,\mathrm {W} \end {equation*} \begin {equation*} t = 3\,\mathrm {min} = 180\,\mathrm {s} \end {equation*} \begin {equation*} E = P \cdot t = 2000\,\mathrm {W} \times 180\,\mathrm {s} = 360\,000\,\mathrm {J} \end {equation*}
• \begin {equation*} m = 5\,\mathrm {kg} \quad (\text {Dichte Wasser} \approx 1\,\mathrm {kg/L}) \end {equation*} \begin {equation*} c = 4186\,\mathrm {\frac {J}{kg \cdot K}} \quad (\text {spezifische Wärmekapazität von Wasser}) \end {equation*} \begin {equation*} \Delta T = 100^\circ \mathrm {C} - 20^\circ \mathrm {C} = 80\,\mathrm {K} \end {equation*} \begin {equation*} Q = m \cdot c \cdot \Delta T = 5\,\mathrm {kg} \times 4186\,\mathrm {\frac {J}{kg \cdot K}} \times 80\,\mathrm {K} = 1\,674\,400\,\mathrm {J} \end {equation*}

5 Energie und Leistung

• \begin {equation*} E = P\cdot t \end {equation*} \begin {equation*} E = 2\,\text {kW} \cdot 3\,\text {h} = 6\,\text {kWh} \end {equation*}
• \begin {equation*} C = E\cdot P \end {equation*} \begin {equation*} C = 6\,\mathrm {kWh} \cdot 0{,}30\,\frac {€}{\mathrm {kWh}} = 1{,}80\,\text {€} \end {equation*}

6 Wirkungsgrad

• \begin {equation*} \eta = \frac {P_{\text {el}}}{P_{\text {mech}}} = \frac {1\,\text {kW}}{1{,}5\,\text {kW}} \approx 0{,}6667 \Rightarrow \eta \approx 66.67\% \end {equation*}
• \begin {equation*} P_{\text {mech}} = \frac {2\,\text {kW}}{0{,}6667} \approx 3\,\text {kW} \end {equation*}