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NEET 2016
Exam
NEET
Year
2016
Subject
Physics
Chapter
Thermal Properties of Matter

NEET 2016 · Physics · Thermal Properties of Matter

A body cools from a temperature 3T to 2T in 10 minutes. The room...

A body cools from a temperature 3T3T to 2T2T in 1010 minutes. The room temperature is TT. Assume that Newton's law of cooling is applicable. The temperature of the body at the end of next 1010 minutes will be

Options

  1. A74T\dfrac{7}{4}T
  2. B32T\dfrac{3}{2}T
  3. C43T\dfrac{4}{3}T
  4. DTT

Correct answer

B. 32T\dfrac{3}{2}T

Step-by-step solution

T1−T2∆t=K(T1+T22−T0)\dfrac{{T}_{1} - {T}_{2}}{∆ t} = K\left(\dfrac{{T}_{1} + {T}_{2}}{2} - {T}_{0}\right)

3T−2T10=K(2.5T−T)\dfrac{3T - 2T}{10} = K\left(2.5T - T\right)

⇒T10=K(1.5)T⇒ \dfrac{T}{10} = K\left(1.5\right)T

K=115K = \dfrac{1}{15}

Now, 2T−x10=K(2T+x2−T)\dfrac{2T - x}{10} = K\left(\dfrac{2T + x}{2} - T\right)

Solving x=3T2x = \dfrac{3T}{2}
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