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# A Body Cools Down from 65°C to 60°C in Minutes. It Will Cool Down from 60°C to 55°C in - Physics

ConceptNewton’s Law of Cooling

#### Question

A body cools down from 65°C to 60°C in minutes. It will cool down from 60°C to 55°C in

•  5 minutes

• less than 5 minutes

• more than 5 minutes

•  less than or more than 5 minutes depending on whether its mass is more than or less than 1 kg.

#### Solution

more than 5 minutes
Let the temperature of the surrounding be T^circ CAverage temperature of the liquid in first case = 62.5^circ
Average temperature difference from the surroundings = (62.5 - T )^circ C
From newton law of cooling,
1° C  min-1 = -bA ( 62.5 - T )°C
⇒ -bA = 1/(62.5 - t) "min"^-1    ...... ( i )
For the second case,
Average temperature = 57.5° C
Temperature difference from the surroundings = ( 57.5 - 7 )° C
From Newton's law of cooling and equation (i),
(5^circ C)/ t = -bA ( 57.5 - T )^circ C

⇒ (5^circ C)/t = 1/(62.5 - t) (57.5 - T )^circ C

⇒ t = (5 ( 62.5 - T ))/ ((57.5 -T ))

⇒ t > 5 \text{minutes}

Is there an error in this question or solution?

#### APPEARS IN

HC Verma Solution for Concepts of Physics - Vol. 2 (2018 to Current)
Chapter 6: Heat Transfer
MCQ | Q: 10 | Page no. 97
Solution A Body Cools Down from 65°C to 60°C in Minutes. It Will Cool Down from 60°C to 55°C in Concept: Newton’s Law of Cooling.
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