Question

The temperature of a room heated by a radiator is ${20}^{o}C$ when the outside temperature is $-{20}^{o}C$ and it becomes ${10}^{o}C$ when the outside temperature is $-{40}^{o}C$. What is the temperature of the radiator?

• A. 50${}^{0}C$
• B. 70${}^{0}C$
• C. 90${}^{0}C$
• D. 60${}^{0}C$

Answer 1

Answer: (D)

60${}^{0}C$

At steady state heat released to room $=$ heat dissipated outside

$T-{20}^0=K[{20}^0-(-{20}^0\left)\right]$ $={40}^{0}K$.........(1)

In the second case,

$T-{10}^0=K[{10}^0-(-{40}^0\left)\right]={50}^{0}K$

$\frac{T-{20}^0}{T-{10}^0}=\frac{4}{5}$

$\Rightarrow T={60}^{0}C$