Question

A circular hole of radius 1 cm is drilled in brass
steel at 293K. What will be the diameter of this
hole when the sheets is heated to 393K? Given :
for brass
6 1 18 10 K

Answer 1

Step-by-step Explanation:

Given: Radius of hole ($R_{T_{1}}$) = 1 cm

The temperature at which brass steel is drilled (T₁) = 293K

Temperature after heating (T₂) = 393K

To Find: Diameter ($D_{T_{2}}$) of the hole after heating

Solution:

• Calculating the diameter of the hole after heating

Diameter $D_{T_{2}}$ at the temperature T₂ is given as-

$D_{T_{2}} = D_{T_{1}} [1+ \alpha (T_{2}-T_{1})]$

where α is the small change in length per unit original length per unit temperature change. For brass, α = 18 × 10⁻⁶ K⁻¹

Substituting the given values in the above formula to get

$\Rightarrow D_{T_{2}} = 2 \times R_{T_{1}} [1 + (18 \times 10^{-6} ) (393 -293)]$

$\Rightarrow D_{T_{2}} = 2 \times (1) [1 + (18 \times 10^{-6} ) (100)]$

$\Rightarrow D_{T_{2}} = 2.0036 \ cm$

Hence, the diameter of the hole after heating the sheet at 393K is $D_{T_{2}} = 2.0036 \ cm$