Verified Solution • 2025–26 Session moderate

QPages 98-102: Q14: HC Verma: Concepts of Physics - Volume 2 Heat Transfer Pages 98-102: Q14 Solution: On a winter day when the atmospheric temperature drops to…

⚠️ Common Exam Traps & Conceptual Pitfalls

When integrating the growth rate $\frac{dx}{dt}=\frac{K\Delta T}{\rho L x}$, students often treat the thickness $x$ as a constant and obtain a linear time dependence. The correct integration yields $t=\frac{\rho L}{2K\Delta T}x^2$, so the time grows with the square of the ice thickness. Remember to keep $x$ in the denominator during integration and square it in the final expression.

On a winter day when the atmospheric temperature drops to _10�C, ice forms on the surface of a lake. a) Calculate the rate of increase of thickness of the ice when 10 cm of the ice is already formed. b) Calculate the total time taken in forming 10 cm of ice. Assume that the temperature of the entire water reaches 0�C before the ice starts forming. Density of water = 1000 kg m−31000 \text{ kg m}^{-3}, latent heat of fusion of ice = 3.36×105 J kg−13.36 \times 10^5 \text{ J kg}^{-1} and thermal conductivity of ice = 1.7 W m−1 �C−11.7 \text{ W m}^{-1} \text{ �C}^{-1}. Neglect the expansion of water on freezing.

Step-by-Step Verified Solution

**Answer:** (a) Rate = 5 _ 10__ m/s (b) Time = 27.45 hours. **Step-by-Step Explanation:** Given: K = 1.7 W/m�C, _ = 1000 kg/m_, L = 3.36 _ 10_ J/kg, _T = 10�C. (a) For ice thickness x = 10 cm: rate = K _T / (x _ L) = 1.7 _ 10 / (0.1 _ 1000 _ 3.36 _ 10_) = 5.06 _ 10__ m/s. (b) Time = _L/(2K_T) _ x_ = (1000 _ 3.36 _ 10_ _ 0.01)/(2 _ 1.7 _ 10) = 9.88 _ 10_ s = 27.45 hours [citation:14].

All Questions in this Chapter

QPage 97: Q1 QPage 97: Q2 QPage 97: Q3 QPage 97: Q4 QPage 97: Q5 QPage 97: Q6 QPage 97: Q7 QPage 97: Q8 QPage 97: Q9 QPage 97: Q10 QPages 96-97: Q1 QPages 96-97: Q2 QPages 96-97: Q3 QPages 96-97: Q4 QPages 96-97: Q5 QPages 96-97: Q6 QPages 96-97: Q7 QPages 96-97: Q8 QPages 96-97: Q9 QPages 96-97: Q10 QPages 96-97: Q11 QPages 97-98: Q1 QPages 97-98: Q2 QPages 97-98: Q3 QPages 97-98: Q4 QPages 97-98: Q5 QPages 97-98: Q6 QPages 98-102: Q1 QPages 98-102: Q2 QPages 98-102: Q3 QPages 98-102: Q4 QPages 98-102: Q5 QPages 98-102: Q6 QPages 98-102: Q7 QPages 98-102: Q8 QPages 98-102: Q9 QPages 98-102: Q10 QPages 98-102: Q11 QPages 98-102: Q12 QPages 98-102: Q13 QPages 98-102: Q14 QPages 98-102: Q15 QPages 98-102: Q16 QPages 98-102: Q17 QPages 98-102: Q18 QPages 98-102: Q19 QPages 98-102: Q20 QPages 98-102: Q21 QPages 98-102: Q22 QPages 98-102: Q23 QPages 98-102: Q24 QPages 98-102: Q25 QPages 98-102: Q26 QPages 98-102: Q27 QPages 98-102: Q28 QPages 98-102: Q29 QPages 98-102: Q30 QPages 98-102: Q31 QPages 98-102: Q32 QPages 98-102: Q33 QPages 98-102: Q34 QPages 98-102: Q35 QPages 98-102: Q36 QPages 98-102: Q37 QPages 98-102: Q38 QPages 98-102: Q39 QPages 98-102: Q40 QPages 98-102: Q41 QPages 98-102: Q42 QPages 98-102: Q43 QPages 98-102: Q44 QPages 98-102: Q45 QPages 98-102: Q46 QPages 98-102: Q47 QPages 98-102: Q48 QPages 98-102: Q49 QPages 98-102: Q50 QPages 98-102: Q51 QPages 98-102: Q52 QPages 98-102: Q53 QPages 98-102: Q54 QPages 98-102: Q55

Related Learning Resources & Exam Preparation

Chapter Practice Bank
Practice all topic-wise questions from Heat Transfer
Reference Textbook Solutions
Explore complete chapter exercises for HC Verma: Concepts of Physics - Volume 2
Competitive PYQ Question Bank
Browse year-wise authentic previous years' questions with solutions
Authentic CBT Mock Tests
Simulate official exam environment with live timer and percentile scoring