Advertisements
Advertisements
Question
A body cools down from 65°C to 60°C in minutes. It will cool down from 60°C to 55°C in
Options
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.
Advertisements
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}`
APPEARS IN
RELATED QUESTIONS
A body cools from 80 °C to 50 °C in 5 minutes. Calculate the time it takes to cool from 60 °C to 30 °C. The temperature of the surroundings is 20 °C.
An ordinary electric fan does not cool the air, still it gives comfort in summer. Explain
A metal sphere cools from 80 °C to 60 °C in 6 min. How much time with it take to cool from 60 °C to 40 °C if the room temperature is 30 °C?
A metal sphere cools from 66° C to 57° C in 10 minutes and to 44° C in the next 10 minutes. The ratio of fall of temperature of first 10 minutes to next ten minutes is ____________.
A liquid with a certain surface area takes 10 minutes to cool from 80° C to 70° C. The time taken by it to cool from 80° C to 60° C is [The surrounding temperature being 40° C] ____________.
Newton's law of cooling leads to the expression:
A tub of hot water cools from 80°C to 75°C in time t1 from 75°C to 70°C in time t2, and from 70°C to 65°C in time t3 then:
Two circular discs A and B with equal radii are blackened. They are heated to the same temperature and are cooled under identical conditions. What inference do you draw from their cooling curves?
A cup of coffee cools from 90°C to 80°C in t minutes, when the room temperature is 20°C. The time taken by a similar cup of coffee to cool from 80°C to 60°C at a room temperature same at 20°C is ______.
Is the bulb of a thermometer made of diathermic or adiabatic wall?
According to Newton's law of cooling, the rate of cooling of the body is proportional to (Δθ), where Δθ is the difference between the temperature of the body and the surroundings, and n is equal to ______.
In 5 minutes, a body cools from 75°C to 65°C at a room temperature of 25°C. The temperature of the body at the end of the next 5 minutes is ______°C.
What is the shape of the cooling curve T vs t?
If we plot \[\frac{dT}{dt}\] vs (T−T₀), what graph do we get?
Why must the surrounding temperature T₀ remain constant in the experiment?
A metal ball cools at 2.0°C/min when its temperature is 60°C and the surrounding temperature is 20°C. What will be its rate of cooling when its temperature drops to 30°C?
