First slide

Radiation

Question

A body cools from 60⁰C to 50⁰C in 10 min. If room temperature is 25⁰C. Temperature of body at the end
of next 10 min, will be [UP CPMT 2012]

Moderate

A

38.5⁰C
B

40⁰C
C

45⁰C
D

42.85⁰C

Solution

Newton's cooling law is given as
$\frac{θ_{1} - θ_{2}}{t} = k (\frac{θ_{1} + θ_{2}}{2} - θ_{0})$
Given, $θ_{0} = 25^{\circ} C, θ_{1} = 60^{\circ} C, t = 10 min and θ_{2} = 50^{\circ} C$
$∴ \frac{60 - 50}{10} = k (\frac{60 + 50}{2} - 25)$
We get, $k = \frac{1}{30} units and t_{2} = 10 \min$
Again, $θ_{2} = θ, θ_{1} = 50^{\circ} C, θ_{0} = 25^{\circ} C$
$∴ (\frac{50 - θ}{10}) = \frac{1}{30} (\frac{50 + θ}{2} - 25)$
$\Rightarrow θ = {42.85}^{\circ} C$

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