If a piece of metal is heated to temperature θand then allowed to cool in a room, which is at te

step 1 In the following question, we are required to find out a graph which will show the relationship

If a piece of metal is heated to temperature θand then...

If a piece of metal is heated to temperature $\theta$ and then allowed to cool in a room, which is at temperature $\theta_{0}$, then the graph between the temperature $T$ of the metal and time $t$ will be closed to
(A)
(B)
(C)
(D)

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Newton’s Law of Cooling

This fundamental principle states that the rate at which an object cools is proportional to the difference between its temperature and the ambient temperature. It forms the basis of the differential equation used to model the cooling process.

Exponential Decay

Exponential decay is a process where a quantity decreases at a rate proportional to its current value. In the context of cooling, it describes how the temperature of the metal reduces over time, following an exponential decline towards the ambient temperature.

Asymptotic Behavior

Asymptotic behavior refers to how a function approaches a specific value without necessarily reaching it. For a cooling object, the graph of temperature versus time will level off as it approaches the ambient temperature, which acts as an asymptote in the cooling curve.

Transcript

Please give Ace some feedback