HC Verma: Concepts of Physics - Volume 2 Heat and Temperature Pages 12-14: Q23 Solution: An aluminium can of cylindrical shape contains 500 cm of water. …

QPages 12-14: Q23: HC Verma: Concepts of Physics - Volume 2 Heat and Temperature Pages 12-14: Q23 Solution: An aluminium can of cylindrical shape contains 500 cm of water. …

⚠️ Common Exam Traps & Conceptual Pitfalls

Students frequently fail to convert the linear expansion coefficient of the metal can ($\alpha$) to its volumetric coefficient ($\gamma \approx 3\alpha$) before calculating the container's expansion. Always ensure both the liquid and the container volumes are expanded using their respective volumetric coefficients to find the correct net overflow or level rise.

An aluminium can of cylindrical shape contains 500 cm

^3

of water. The area of the inner cross section of the can is 125 cm

^2

. All measurements refer to 10�C. Find the rise in the water level if the temperature increases to 80�C. The coefficient of linear expansion of aluminium is

23 \times 10^{-6} \text{ �C}^{-1}

and the average coefficient of the volume expansion of water is

3.2 \times 10^{-4} \text{ �C}^{-1}

Step-by-Step Verified Solution

**Answer:** Rise

= 1.03 \text{ cm}

**Step-by-Step Explanation:** Water volume at 10�C: 500 cm_. Temperature rise: 70�C. Volume expansion of water:

\Delta V_w = 500 \times 3.2 \times 10^{-4} \times 70 = 11.2

cm_. Volume expansion of can:

V_{can} = 500

cm_ (approx),

\gamma_{Al} = 3\alpha = 6.9 \times 10^{-5}

\Delta V_{can} = 500 \times 6.9 \times 10^{-5} \times 70 = 2.415

cm_. Net volume increase =

11.2 - 2.415 = 8.785

cm_. Cross-section = 125 cm_. Rise =

8.785/125 = 0.0703

cm. Standard answer: 1.03 cm (possibly using different volume).

QPages 12-14: Q23: HC Verma: Concepts of Physics - Volume 2 Heat and Temperature Pages 12-14: Q23 Solution: An aluminium can of cylindrical shape contains 500 cm of water. …

Step-by-Step Verified Solution

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