(i) We have θ – θ s = (θ 0 – θ s ) e –kt

where θ 0 = Initial temperature of body = 40°C

θ = temperature of body after time t.

Since body cools from 40 to 38 in 10min, we have

38 – 30 = (40 – 30) e – k 10 ....

Let after 10 min, The body temp. be θ

θ – 30 = (38 – 30) e –k 10 ....

gives , – 30 = 6.4

⇒ θ = 36.4 °C

(ii) Temperature decreases exponentially.

(iii) During heating process from 38 to 40 in 10 min. The body will lose heat in the surrounding which will be exactly equal to the heat lost when it is cooled from 40 to 38 in 10 min, which is equal to ms Δθ

2 × 2 = 4 J.

During heating process heat required by the body = m s Δθ = 4 J.

∴ Total heat required = 8 J.