Question

A sheet of solid material having area \(A\) and coefficient of linear expansion \(\alpha\). The mass of sheet is \(m\) and specific heat capacity is \(s\). If \(dQ\) is the amount of heat given to the sheet then change in its area is

• A. \(\frac{A(2\alpha )ms}{\Delta Q}\)
• B. \(\frac{A(2\alpha )\Delta Q}{ms}\)
• C. \(\frac{A\alpha \Delta Q}{ms}\)
• D. \(\frac{A\alpha ms}{\Delta Q}\)

Hint:

Find the temperature rise from the heat supplied, then use area expansion with coefficient twice the linear coefficient.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept
Heat supplied gives a temperature rise \(\Delta T=\dfrac{\Delta Q}{ms}\).
Area expansion uses \(\beta=2\alpha\).

Step 2: Area change
\(\Delta A=A\beta\Delta T=A(2\alpha)\Delta T\).

Step 3: Substitute
\(\Delta A=\dfrac{A(2\alpha)\Delta Q}{ms}\).

Step 4: Compare the options
This is option (B).

Final Answer:
The change in area is 2 alpha A delta Q divided by m s. \[ \boxed{\text{(B) }\dfrac{A(2\alpha)\Delta Q}{ms}} \]