Question

if a plate having a hole of radius 1cm at 20 degree Celsius is heated up to 100 degree Celsius. What will be the radius of hole​

Answer 1

Answer:

d_2= 0.001359 cm

Explanation:

Considering the plate to be copper , the coefficient of thermal expansion of copper = 1.70×10^(-5) 1/K

for the coefficient of superficial expansion β, the change in temp ΔT is given As

change in area (ΔA)/ original area A= βΔT

also β= 2α

therefore,

$\frac{d_2^2-d_1^2}{d_1^2}= 2\alpha\delta T$

now putting d_1= 2 cm , T_1= 20 ° C and T_2= 100° C

$\frac{d_2^2}{d_1^2}-1= 2\alpha\delta (T_2-T_1)$

there fore, d_2= 2.002718 cm

change in diameter= 2.002718-2= 0.002718 cm

therefore radius increases by 0.001359 cm