Question

The room heater can maintain only ${16}^{0}C$ temperature in the room when the temperature of outside is ${20}^{0}C$. It is not warm and comfortable that is why the electric stove with power of 1KW is also plugged in. Together these two devices maintain the room temperature of ${22}^{0}C$. Find thermal power of heater in KW.

Answer 1

Rate of heat loss with only room heater

$P_h=\frac{\Delta Q}{\Delta t}=C(16+20)$ where C = constant.

$P_h+P_s=\left(\frac{\Delta Q^{\prime }}{\Delta t}\right)=C(22+20)$ for heater plus stove

$\frac{P_h}{P_h+P_s}=\frac{36}{42}\Rightarrow 7P_h=6P_h+6P_s$

$P_h=6P_s=6\times 1=6KW$