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Internal energy is a property or state function in thermodynamics that defines the energy of a material in the absence of capillary effects and external electric, magnetic, and other fields.

The temperature difference determines the pace at which heat energy is transmitted between two systems,$P鈭�鈭�T$ where the value of P is the rate of transfer of heat energy and the value $鈭�T$of is the temperature difference.

Power is the average energy leaked per second that is given by:

$P=\frac{E_1}{t}$.

Substitute $E_1=45kWh$and $t=3h$into the above formula.

$$\begin{gathered} P=\frac{45kWh}{3h} \\ =15kW \\ =\left(15kW\right)\left(\frac{1000J/s}{1kW}\right) \\ =15,000J/s \end{gathered}$$

Therefore, the power is 15,000J/s .

Find the difference in temperature of inside and outside in first case.

$$\begin{gathered} 鈭�T_1=T_1-T_0 \\ ={20}^{0}C-0^{0}C \\ ={20}^{0}C \end{gathered}$$

Find the difference in temperature of inside and outside in the second case.

$$\begin{gathered} 鈭�T_2=T_2-T_0 \\ ={25}^{0}C-0^{0}C \\ ={25}^0 \end{gathered}$$

Write the equation for electrical energy spent in the second situation.

$$\begin{gathered} P鈭�鈭�Tn \\ \frac{E}{t}鈭�鈭�Tn \\ E鈭�鈭�Tn \end{gathered}$$

Divide $E_2$by $E_1$by using the obtained result.

$$\begin{gathered} \frac{E_2}{E_1}=\frac{鈭�T_2}{鈭�T_1} \\ {E}_2=\left(\frac{鈭�T_2}{鈭�T_1}\right)E_1 \end{gathered}$$

Substitute $鈭�T_2={25}^{0}C$$鈭�T_1={20}^{0}C$, and $E_1=45kWh$into the obtained equation.

role="math" localid="1657949205869" $$\begin{gathered} E_2=\left(\frac{{25}^{0}C}{{20}^{0}C}\right)\left(45kwh\right) \\ =56.3kwh \end{gathered}$$

Therefore, the energy consumed is $56.3kwh$.