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.
On a hot summer day we want to cool our room by opening the refrigerator door and closing all the windows and doors. Will the process work?
On a cold winter night you are asked to sit on a chair. Would you like to choose a metal chair or a wooden chair? Both are kept in the same lawn and are at the same temperature.
The temperature of the atmosphere at a high altitude is around 500°C. Yet an animal there would freeze to death and not boil. Explain.
Newton's law of cooling is a special case of
Answer the following question.
State Newton’s law of cooling and explain how it can be experimentally verified.
Solve the following problem.
A metal sphere cools at the rate of 0.05 ºC/s when its temperature is 70 ºC and at the rate of 0.025 ºC/s when its temperature is 50 ºC. Determine the temperature of the surroundings and find the rate of cooling when the temperature of the metal sphere is 40 ºC.
Rate of cooling of a body is 0.4 °C/min when excess temperature is 20 °C. The proportionality constant 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] ____________.
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 glass full of hot milk is poured on the table. It begins to cool gradually. Which of the following is correct?
- The rate of cooling is constant till milk attains the temperature of the surrounding.
- The temperature of milk falls off exponentially with time.
- While cooling, there is a flow of heat from milk to the surrounding as well as from surrounding to the milk but the net flow of heat is from milk to the surounding and that is why it cools.
- All three phenomenon, conduction, convection and radiation are responsible for the loss of heat from milk to the surroundings.
One day in the morning, Ramesh filled up 1/3 bucket of hot water from geyser, to take bath. Remaining 2/3 was to be filled by cold water (at room temperature) to bring mixture to a comfortable temperature. Suddenly Ramesh had to attend to something which would take some times, say 5-10 minutes before he could take bath. Now he had two options: (i) fill the remaining bucket completely by cold water and then attend to the work, (ii) first attend to the work and fill the remaining bucket just before taking bath. Which option do you think would have kept water warmer? Explain.
According to Newton's law of cooling, how does the rate of cooling depend on temperature?
In \[\frac{dT}{dt}\] = C(T−T₀), what does the constant C represent?
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?
A metal sphere cools in a room at 30°C. At T = 70°C, dT/dt = −1.6°C/min. Find C.
Why is the calorimeter kept in open air or a constant-temperature enclosure during Newton’s law of cooling 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?
