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Increase in volume or area of a heated cube or sheet

This type of question, asked 3 times: 2021 Paper 1, 25 Jun 2022, 4 Apr 2025. All 3 questions below, oldest first.

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  1. Question 1

    2021 Paper 1

    20
    Each side of a box made of metal sheet in cubic shape is ' aa ' at room temperature ' TT ', the coefficient of linear expansion of the metal sheet is ' α\alpha '. The metal sheet is heated uniformly, by a small temperature ΔT\Delta T, so that its new temperature is T+ΔTT+ \Delta T. Calculate the increase in the volume of the metal box-

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  2. Question 2

    25 Jun 2022

    94
    A solid metallic cube having total surface area 24 m2m^{2} is uniformly heated. If its temperature is increased by 10∘C10^{\circ}C, calculate the increase in volume of the cube ( Given: α=5.0×10−4 ∘C−1\alpha = 5.0 \times10^{- 4}\ ^{\circ}C^{- 1} )

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  3. Question 3

    4 Apr 2025

    78
    Consider a rectangular sheet of solid material of length l=9 cm\mathcal{l}= 9\text{ }cm and width d=d = 4 cm4\text{ }cm. The coefficient of linear expansion is α=3.1×10−5 K−1\alpha= 3.1 \times10^{- 5}{\text{ }K}^{- 1} at room temperature and one atmospheric pressure. The mass of sheet m=0.1 kgm= 0.1\text{ }kg and the specific heat capacity Cv=900 J kg−1 K−1C_{v}= 900\text{ }J{\text{ }kg}^{- 1}{\text{ }K}^{- 1}. If the amount of heat supplied to the material is 8.1×102 J8.1 \times10^{2}\text{ }J then change in area of the rectangular sheet is :-

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