Question

A substance takes 3 minute in cooling from 50°c to 45°c and takes 5 minute in cooling 45°c to 40°c what is the temperature of the surrounding?​

Answer 1

Answer:

Explanation:

I jumped steps at the end, hope it'll be helpful.

Answer 2

Given:

Time taken to cool from 50°C to 45°C = 3 minutes

Time taken to cool from 45°C to 40°C = 5 minutes

To find:

Temperature of the surroundings.

Solution:

Let the temperature of the surroundings be T.

By Newton's laws of cooling:

dθ/dt = -k(θ - θ₀)

θ is the average temperature of the substance.

θ₀ is the temperature of the surroundings.

Average temperature = (50+45)/2 = 47.5

Putting the values we get:

(50-45)/3 = -k(47.5 - T)

5/3 = -k(47.5 - T)     (1)

For the next step:

Average temperature = (45+40)/2 = 42.5

(45-40)/ 5 = -k(42.5 - T)

1 = -k(42.5 - T)      (2)

Dividing both the equations we get:

5/3 = (47.5 - T) / (42.5 - T)

5(42.5 - T) = 3(47.5 - T)

212.5 - 5T = 142.5 -3T

2T = 212.5 - 142.5

2T = 70

T = 35°C

Therefore the temperature of the surroundings will be 35°C.