Question

It is known for a certain liquid that it takes $70s$ to cool from $55^{o}C$ to $50^{o}C$ and $30s$ to cool from $95^{o}C$ to $90^{o}C$ . Figure out the ambient temperature of the room.

• A. $16.5^{o}C$
• B. $22.5^{o}C$
• C. $28.5^{o}C$
• D. $32.5^{o}C$

Answer 1

Answer: (B)

If the temperature of body decreases from $T_1$ and $T_2$ and temperature of surroundings is $T_o$ then according to Newton's law of cooling :
Average excess of temperature = $\left[\frac{T_1+T_2}{2}-T_o\right]$
$\Rightarrow \left[\frac{T_1-T_2}{t}\right]=K\left[\frac{T_1+T_2}{2}-T_o\right]$
$\Rightarrow \frac{95-90}{30}=k\left[\frac{95+90}{2}-T_0\right]$
$\Rightarrow \frac{55-50}{70}=k\left[\frac{55+50}{2}-T_0\right]$
On dividing both the equations ,we get
$T_0=22.5^{\circ }C$