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NTA Abhyas 2020

Exam: NTA Abhyas
Year: 2020
Subject: Physics
Chapter: Thermal Properties of Matter

NTA Abhyas 2020 · Physics · Thermal Properties of Matter

A body cools from 50 ° C to 40 ° C in 5 minutes. Its temperature...

A body cools from

50 ° C

to

40 ° C

in

5

minutes. Its temperature comes down to

33. 33 ° C

in the next

5

minutes. The temperature of the surroundings is

Options

A $15 ℃$
B $20 ℃$
C $25 ℃$
D $10 ℃$

Correct answer

B. $20 ℃$

Step-by-step solution

Using Newton's law of cooling,

log

\dfrac{{\theta}_{2} - {\theta}_{0}}{{\theta}_{1} - {\theta}_{0}} = - Kt

log

\dfrac{40 - {\theta}_{0}}{50 - {\theta}_{0}} = - K \times 5

.....(i)

log

\dfrac{33.33 - {\theta}_{0}}{40 - {\theta}_{0}} = - K \times 5

.....(ii)

From Eqs.(i) and (ii),

\dfrac{40 - {\theta}_{0}}{50 - {\theta}_{0}} = \dfrac{33.33 - {\theta}_{0}}{40 - {\theta}_{0}}

On solving, we get

{\theta}_{0} = 19.95℃ \approx 20℃

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