Chapter 13, Problem 10P

To what temperature would you have to heat a brass rod for it to be 1.5% longer than it is at 25 C?

To determine

The temperature to which a brass rod has to be heated from 25°C for the given increase in length to take place

Answer to Problem 10P

Solution:

The temperature to which the brass rod has to be heated is 814.5°C.

Explanation of Solution

Given:

Initial temperature of the brass rod, $T_0=25°C$

If l₀ is the temperature at T₀, increase in length, $\Delta l=1.5\%of{l}_0=0.015l_0$

Formula used:

$\Delta l=l\times \alpha \times \Delta T$, where α is the coefficient of linear expansion of a material.

Calculation:

The relation between change in length of a substance and change in temperature is given by,

$\Delta l=l_0\times \alpha \times \Delta T$---(i),

Where, ΔT is the change in temperature andα is the coefficient of linear expansion of a material.

For brass, $\alpha =19\times 10-6/°C$

$\Delta T=Tf–T_0$,

Where, T_f is the required temperature

Substituting the known values in equation (i), we have

$0.015l_0=l_0\times 19\times 10-6/°C\times \left(T_f-25°C\right)$

or $T_f-25°C=\frac{0.015l{}_0}{l_{0}x19x{10}^{-6}/°C}$

or $T_f-25°C=789.5°C$

or $T_f=814.5°C$