Question

The room temperature is $+{20}^{\circ }C$ when outside temperature is $-{20}^{\circ }C$. Room temperature is $+{10}^{\circ }C$ when outside temperature is $-{40}^{\circ }C$. The temperature of the radiator heating the room is:

• A. ${70}^{\circ }C$
• B. ${60}^{\circ }C$
• C. ${50}^{\circ }C$
• D. ${40}^{\circ }C$

Answer 1

The correct option is B ${60}^{\circ }C$

Since the heat inflow at steady state must be equal to heat outflow. Hence, from Newton's Law of cooling,

$\frac{(T-20)}{dt}=k(20-(-20\left)\right)$

Also, $\frac{(T-10)}{dt}=k(10-(-40\left)\right)$

Hence, $\frac{T-20}{T-10}=\frac{4}{5}$

Thus, $T={60}^{0}C$