First slide

Radiation

Question

A liquid cools from 50°C to 45°C in 5 minutes and from 45 to 41.5°C in the next 5 minutes. The temperature of the surrounding is

Easy

A

27°C
B

40.3°C
C

23.3°C
D

33.3°C

Solution

According to Newton's law of cooling
$ms (\frac{θ_{1} - θ_{2}}{t}) \propto [\frac{θ_{1} + θ_{2}}{2} - θ_{0}]$
where $θ_{2}$ = temperature of surroundings.
In first case,
$ms (\frac{50 - 45}{5}) \propto [\frac{50 + 45}{2} - θ_{0}] . . . . . (1)$
In second case,
$ms (\frac{45 - 41 \cdot 5}{5}) \propto [\frac{45 + 41 \cdot 5}{2} - θ_{0}] . . . . (2)$
Solving eqs, (1) and (2), we get
$θ_{0} = 33 \cdot 3^{\circ} C$

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