If a piece of metal is heated to temperature θ and then allowed to cool in a room which is at temperature θ 0 , the graph between the temperature T of the metal and time t will be closest to :

Step-by-step solution

According to Newton's cooling law, rate of cooling is d θ d t ∝ θ - θ 0 Here, θ = the temperature of the body θ 0 = Room temperature(constant) Let k be the proportionality constant and θ i be the initial temperature. Therefore, d θ d t = - k θ - θ 0 ⇒ ∫ d θ θ - θ 0 = - k ∫ d t ⇒ ln θ - θ 0 = - k t ⇒ θ = θ 0 + θ - θ 0 e - k t Hence, the graph is exponential.