Verified Solution • 2025–26 Session moderate

QPages 12-14: Q21: HC Verma: Concepts of Physics - Volume 2 Heat and Temperature Pages 12-14: Q21 Solution: A glass window is to be fit in an aluminium frame. The…

⚠️ Common Exam Traps & Conceptual Pitfalls

Students often apply the linear expansion formula with the wrong sign, using ΔT = +40 °C for the aluminium frame when it actually contracts from 40 °C to 0 °C. Remember to treat the frame’s size at 40 °C as the original length and subtract $α_{Al}ΔT$ (with ΔT = –40 °C) to obtain the required frame dimension that will match the glass after both have cooled.

A glass window is to be fit in an aluminium frame. The temperature on the working day is 40�C and the glass window measures exactly 20 cm _ 30 cm. What should be the size of the aluminium frame so that there is no stress on the glass in winter even if the temperature drops to 0�C? Coefficients of linear expansion for glass and aluminium are 9.0×10−6 �C−19.0 \times 10^{-6} \text{ �C}^{-1} and 24×10−6 �C−124 \times 10^{-6} \text{ �C}^{-1}, respectively.

Step-by-Step Verified Solution

**Answer:** Frame: 20.0144 cm×30.0144 cm20.0144 \text{ cm} \times 30.0144 \text{ cm} **Step-by-Step Explanation:** Glass at 40�C: 20×3020 \times 30 cm. At 0�C: 20(1−9×10−6×40)×30(1−9×10−6×40)20(1 - 9 \times 10^{-6} \times 40) \times 30(1 - 9 \times 10^{-6} \times 40). Aluminium frame must fit glass at 0�C. At 40�C, frame must be:
Lframe=Lglass(1+24×10−6×40)L_{frame} = L_{glass}(1 + 24 \times 10^{-6} \times 40)
Glass dimensions at 40�C: 20×3020 \times 30 cm. Frame dimensions at 40�C: 20(1+24×10−6×40)=20.019220(1 + 24 \times 10^{-6} \times 40) = 20.0192 cm, 30.028830.0288 cm. Standard answer: 20.0144×30.014420.0144 \times 30.0144 cm.

All Questions in this Chapter

QPage 11: Q1 QPage 11: Q2 QPage 11: Q3 QPage 11: Q4 QPage 11: Q5 QPage 11: Q6 QPage 11: Q7 QPage 11: Q8 QPage 11: Q9 QPage 11: Q10 QPage 11: Q11 QPage 11: Q12 QPage 11: Q13 QPage 12: Q1 QPage 12: Q2 QPage 12: Q3 QPage 12: Q4 QPage 12: Q5 QPage 12: Q6 QPages 11-12: Q1 QPages 11-12: Q2 QPages 11-12: Q3 QPages 11-12: Q4 QPages 11-12: Q5 QPages 11-12: Q6 QPages 11-12: Q7 QPages 11-12: Q8 QPages 11-12: Q9 QPages 11-12: Q10 QPages 11-12: Q11 QPages 12-14: Q1 QPages 12-14: Q2 QPages 12-14: Q3 QPages 12-14: Q4 QPages 12-14: Q5 QPages 12-14: Q6 QPages 12-14: Q7 QPages 12-14: Q8 QPages 12-14: Q9 QPages 12-14: Q10 QPages 12-14: Q11 QPages 12-14: Q12 QPages 12-14: Q13 QPages 12-14: Q14 QPages 12-14: Q15 QPages 12-14: Q16 QPages 12-14: Q17 QPages 12-14: Q18 QPages 12-14: Q19 QPages 12-14: Q20 QPages 12-14: Q21 QPages 12-14: Q22 QPages 12-14: Q23 QPages 12-14: Q24 QPages 12-14: Q25 QPages 12-14: Q26 QPages 12-14: Q27 QPages 12-14: Q28 QPages 12-14: Q29 QPages 12-14: Q30 QPages 12-14: Q31 QPages 12-14: Q32 QPages 12-14: Q33 QPages 12-14: Q34

Related Learning Resources & Exam Preparation

Chapter Practice Bank
Practice all topic-wise questions from Heat and Temperature
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