Share
Notifications

View all notifications

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

Login
Create free account


      Forgot password?

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 C`Average 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.
S
View in app×