Newton's Law of Cooling - UNSOLVED PRACTICE SET

Q7. State Newton's law of cooling. Write its mathematical expression and explain each term.

Q8. A body cools from 60°C to 50°C in 10 minutes when the surroundings are at 20°C. Using Newton's law, calculate the time to cool from 50°C to 40°C.

Q9. Why does a hot body cool faster when the surrounding temperature is lower?

Q10. In your school, a student notices that a cup of hot milk cools faster when placed near a fan than when kept in still air. Explain using Newton's law of cooling.

Q11. Derive the expression T = T₀ + (Tᵢ − T₀)e^(−Kt) from Newton's law of cooling.

Q12. Why is Newton's law of cooling not applicable when the temperature difference between the body and surroundings is very large?

Q13. State and explain Newton's law of cooling. Derive the expression for temperature as a function of time. Discuss:

(i) The conditions under which the law is valid

(ii) How to verify the law experimentally

(iii) The physical significance of the cooling constant K

(iv) Applications in forensic science and engineering

(v) Why the law is a good approximation for radiative cooling at small temperature differences

Q14. A body cools from 90°C to 80°C in 5 minutes, and from 80°C to 70°C in 8 minutes. The surrounding temperature is 30°C.

(a) Verify whether Newton's law of cooling holds for this body.

(b) Calculate the cooling constant K.

(c) Calculate the time to cool from 70°C to 60°C.

(d) Calculate the temperature of the body after 20 minutes from the start.

(e) Discuss why the cooling time increases as the body approaches room temperature.

Q15. Analyse the following cooling situations:

(i) A hot iron rod cooling in air

(ii) A cup of coffee with and without a lid

(iii) A body cooling in vacuum vs. in air

For each case, discuss:

(a) Whether Newton's law applies

(b) The dominant mode of heat transfer

(c) Factors that would increase or decrease the cooling rate

Q16. A body at 100°C is placed in surroundings at 20°C. It cools to 80°C in 10 minutes.

(a) Using Newton's law of cooling, calculate the temperature after 20 minutes.

(b) Calculate the time to cool to 60°C.

(c) Calculate the time to cool to 40°C.

(d) Plot a rough graph of temperature vs time.

(e) Discuss whether the body will ever reach exactly 20°C.

Q17. In a school experiment, students verify Newton's law of cooling using a calorimeter filled with hot water:

Table

Time (min) 0 5 10 15 20 25

Temperature (°C) 80 70 62 55 49 44

Room temperature = 25°C

(a) Calculate (T − T₀) at each time.

(b) Plot log(T − T₀) vs time and verify if it is a straight line.

(c) From the slope, calculate the cooling constant K.

(d) Predict the temperature at t = 30 minutes.

(e) Discuss why the graph might deviate from a straight line at longer times.

Q18. A forensic expert uses Newton's law of cooling to estimate the time of death. A body is found at 30°C in a room at 20°C. The normal body temperature is 37°C.

(a) Assuming Newton's law with K = 0.05 min⁻¹, calculate the time since death.

(b) If the room temperature were 15°C instead, how would this affect the estimate?

(c) Discuss why this method gives only an approximate time of death.

(d) List three factors that could make the estimate inaccurate.

(e) Suggest an improved method for forensic temperature analysis.