A body cools from a temperature 3 to 2 in 10 minute. The room temperature is . The temperature of the body at the end of the next 10 minute is ' x '. Assuming that Newton's law of cooling is applicable, the value of ' x ' will be

Step-by-step solution

According to Newton's law of cooling, the temperature T of a body at time t is given by: T - T₀ = (T_i - T₀)e^ -kt where T₀ is the surrounding temperature and T_i is the initial temperature. For the first 10 minutes, T_i = 3 , T = 2 , and T₀ = : 2 - = (3 - )e^ -10k = 2 e^ -10k e^ -10k = 1 2 For the next 10 minutes, the new initial temperature is T_i = 2 and the final temperature is x : x - = (2 - )e^ -10k x - = ( 1 2 ) x = + 2 = 3 2 Answer: 3 2