JEE Mains · Physics · STD 11 - 10.1, thermonetry,thermal expansion and calorimetry
A solid metallic cube having total surface area \(24\;m ^{2}\) is uniformly heated. If its temperature is increased by \(10\,^{\circ} C\), calculate the increase in volume of the cube \(\left(\right.\) Given \(\left.: \alpha=5.0 \times 10^{-4}{ }^{\circ} C ^{-1}\right)\)
- 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 \(4.8 \times 10^{5} cm ^{3}\)
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 \(24=6 a ^{2} \quad a =2 m\) \(Volume \,V _{0}=(2)^{3}=8 m ^{3}\)…
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