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Physics Question 31 – JEE-MAIN 2025

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Consider a rectangular sheet of solid material of length l=9 cm and width d=4 cm. The coefficient of linear expansion is α=3.1×10−5K−1 at room temperature and one atmospheric pressure. The mass of sheet m=0.1 kg and the specific heat capacity Cv=900 J kg−1K−1. If the amount of heat supplied to the material is 8.1×102 J then change in area of the rectangular sheet is :

The heat supplied to the material will cause a temperature increase, which in turn leads to thermal expansion of its dimensions.

Step 1: Calculate initial area and temperature change✦ Active

First, convert the given dimensions to meters and calculate the initial area A0 of the rectangular sheet. Then, use the heat supplied Q, mass m, and specific heat capacity Cv to find the temperature change ΔT.

l=9 cm=0.09 m d=4 cm=0.04 m A0=l×d=(0.09 m)×(0.04 m)=0.0036 m2=3.6×10−3 m2 Q=mCvΔT⟹ΔT=QmCv ΔT=8.1×102 J(0.1 kg)×(900 J kg−1K−1)=81090 K=9 K
Step 2: Calculate the coefficient of area expansion○ Expand

The coefficient of area expansion β is related to the coefficient of linear expansion α by the formula β=2α for isotropic materials.

α=3.1×10−5 K−1 β=2α=2×(3.1×10−5 K−1)=6.2×10−5 K−1
Step 3: Calculate the change in area○ Expand

Finally, calculate the change in area ΔA using the initial area A0, the coefficient of area expansion β, and the temperature change ΔT.

ΔA=A0βΔT ΔA=(3.6×10−3 m2)×(6.2×10−5 K−1)×(9 K) ΔA=(3.6×6.2×9)×10−8 m2 ΔA=200.88×10−8 m2 ΔA≈2.0×10−6 m2
💡 Teacher's Secret Hint

Ensure all units are consistent (SI units) throughout the calculation to avoid errors.

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