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Imagine a system, that can keep the room temperature within a narrow range between \( 20^{\circ} \mathrm{C} \) to \( 25^{\circ} \mathrm{C} \). the system includes a heat engine operating with variable power \( P=3 K T \), where \( K \) is a constant coefficient, depending upon the thermal insulation of the room, the area of the walls and the thickness of the walls. \( T \) is temperature of the room in degree. when the room temperature drops lower than \( 20^{\circ} \mathrm{C} \), the engine turns on, when the temperature increase over \( 25^{\circ} \mathrm{C} \), the engine turns off, room looses energy at a ate of \( K\left(T-T_{0}\right) \) is the outdoor temperature. The heat capacity of the room is \( C \).

Given \( \left(T_{0}=10^{\circ} C, \ln \left(\frac{3}{2}\right)=0.4, \ln \left(\frac{6}{5}\right)=0.18, \frac{C}{K}=750\right. \) SI-unit)
Suppose at \( t=0 \), the engine turns off, after how much time interval, again, the engine will turn on :
(A) 10 minute
(B) 5 minute
(C) \( 1.125 \) minute
(D) \( 2.25 \) minute
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