MHT CET · Physics · Thermal Properties of Matter
What is change in volume of an iron sphere of volume \(500 \mathrm{~cm}^3\), when it is heated from \(0^{\circ} \mathrm{C}\) to \(\left(\alpha_{\text {Iron }}=12 \times 10^{-6 /{ }^{\circ}} \mathrm{C}\right)\) ?
- A \(1.8 \mathrm{~cm}^3\)
- B \(2 \mathrm{~cm}^3\)
- C \(1.4 \mathrm{~cm}^2\)
- D \(3 \mathrm{~cm}^3\)
Answer & Solution
Correct Answer
(A) \(1.8 \mathrm{~cm}^3\)
Step-by-step Solution
Detailed explanation
\(\frac{\text { Change in Vol. }}{\text { Original Vol. }}=\) Coe. of vol. expansion \(\times\) temp change
\( \Rightarrow \Delta V=V \times\left(3 \alpha_{\text {Iron }}\right) \times(\Delta T) \)
\( \Rightarrow \Delta V=500 \mathrm{~cm}^3 \times\left[3 \times\left(12 \times 10^{-6 /{ }^{\circ}} \mathrm{C}\right)\right] \times\left(100^{\circ} \mathrm{C}\right) \)
\( \Delta V=500 \times 3.6 \times 10^{-3} \mathrm{~cm}^3=1.8 \mathrm{~cm}^3\)
\( \Rightarrow \Delta V=V \times\left(3 \alpha_{\text {Iron }}\right) \times(\Delta T) \)
\( \Rightarrow \Delta V=500 \mathrm{~cm}^3 \times\left[3 \times\left(12 \times 10^{-6 /{ }^{\circ}} \mathrm{C}\right)\right] \times\left(100^{\circ} \mathrm{C}\right) \)
\( \Delta V=500 \times 3.6 \times 10^{-3} \mathrm{~cm}^3=1.8 \mathrm{~cm}^3\)
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