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JEE Mains · Physics · STD 11 - 10.1, thermonetry,thermal expansion and calorimetry

एक ठोस पदार्थ की एक आयताकार चादर पर विचार कीजिए जिसकी लंबाई \(\ell=9 \mathrm{~cm}\) और चौड़ाई \(\mathrm{d}=4 \mathrm{~cm}\) है। कक्ष ताप और एक वायुमंडलीय दाब पर इसका रेखीय प्रसार गुणांक \(\alpha=3.1 \times 10^{-5} \mathrm{~K}^{-1}\) है। चादर का द्रव्यमान \(\mathrm{m}=0.1 \mathrm{~kg}\) और विशिष्ट ऊष्मा धारिता \(\mathrm{C}_{\mathrm{v}}=900 \mathrm{~J} \mathrm{~kg}^{-1} \mathrm{~K}^{-1}\) है। यदि पदार्थ को दी गई ऊष्मा की मात्रा \(8.1 \times 10^2 \mathrm{~J}\) है, तो आयताकार चादर के क्षेत्रफल में परिवर्तन होगा :-

A \(2.0 \times 10^{-6} \mathrm{~m}^2\)
B \(3.0 \times 10^{-7} \mathrm{~m}^2\)
C \(6.0 \times 10^{-7} \mathrm{~m}^2\)
D \(4.0 \times 10^{-7} \mathrm{~m}^2\)

Verified Solution

Answer & Solution

Correct Answer

(A) \(2.0 \times 10^{-6} \mathrm{~m}^2\)

Step-by-step Solution

Detailed explanation

\(\begin{aligned} & \Delta \mathrm{Q}=\mathrm{ms} \Delta \mathrm{T} \\ & 8.1 \times 10^2=0.1 \times 900 \times \Delta \mathrm{T} \\ & \Delta \mathrm{A}=\mathrm{A}_0 2 \alpha \Delta \mathrm{~T}=2.0 \times 10^{-6} \mathrm{~m}^2\end{aligned}\)

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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