Transformer 20073

The transformer is oil-cooled and transforms a power of 20MW with an efficiency of 92%. Determine the temperature of the oil at the outlet of the transformer if the oil was 20°C when it entered the transformer. 2.5 liters of oil will flow through the transformer in 1 second. The density of the oil is 960kg/m³, and the specific heat capacity of the oil is 2.09KJ×kg^-1×K^-1.

Correct answer:

t =  338.9793 °C

Step-by-step explanation:

$$\begin{gathered} q=1-0.92=0.08 \\ P=20\cdot 10^6\cdot q=20\cdot 10^6\cdot \frac{2}{25}=1600000\text{W} \\ {t}_0=20\text{°C} \\ c=2.09\cdot 1000=2090\text{J/kg/°C} \\ \rho =960{\text{kg/m}}^3 \\ V=2.5\text{l}\to {\text{m}}^3=2.5:1000{\text{m}}^3=0.0025{\text{m}}^3 \\ m=\rho \cdot V=960\cdot \frac{1}{400}=\frac{960\cdot 1}{400}=\frac{960}{400}=\frac{12}{5}=2.4\text{kg} \\ E=PT \\ T=1\text{s} \\ E=P\cdot T=1600000\cdot 1=1600000\text{J} \\ E=mc(t-t_0) \\ t=t_0+\frac{E}{m\cdot c}=20+\frac{1600000}{\frac{12}{5}\cdot 2090}=338.9793\text{°C} \end{gathered}$$

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