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

\(24\, m ^{2}\) જેટલો કુલ સપાટી ક્ષેત્રફળ ધરાવતા ધન ધાત્વીય ધનને નિયમિત રીતે ગરમ કરવામાં આવે છે. જો તેનું તાપમાન \(10^{\circ} C\), જેટલું વધારવામાં આવે તો ધનના કદમાં થતો વધારો ગણો. \(\left(\alpha=5.0 \times 10^{-4}{ }^{\circ} C ^{-1}\right)\).

A \(2.4 \times 10^{6} cm ^{3}\)
B \(1.2 \times 10^{5} cm ^{3}\)
C \(6.0 \times 10^{4} cm ^{3}\)
D \(4.8 \times 10^{5} cm ^{3}\)

Verified Solution

Answer & Solution

Correct Answer

(B) \(1.2 \times 10^{5} cm ^{3}\)

Step-by-step Solution

Detailed explanation

Increase in volume \(\Delta V =\gamma V _{0} \Delta T\) \(\gamma=3 \alpha\) So \(\Delta V =(3 \alpha) V _{0} \Delta T\) Total surface area \(=6 a ^{2}\), where \(a\) is side length \(24=6 a ^{2} \quad a =2 m\) \(Volume \,V _{0}=(2)^{3}=8 m ^{3}\)…

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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