Question

The volume of a metal sphere is 1000cm at 273k. What would be it's volume at 373k?
Given: coefficient of linear expansion of metal is 18×10to the power -6

Answer 1

The volume at 373 k=1005.4 cubic centimeter.

Step-by-step explanation:

Coefficient of linear expansion=$\alpha=18\times 10^{-6}$/k

Volume of metal sphere at 273 K=1000 cubic centimeter

Coefficient of volume expansion=$\gamma=3\alpha$

Coefficient of volume expansion=$3\times 18\times 10^{-6}$/k

Coefficient of volume expansion=$54\times 10^{-6}$/k

$T_1=273 k,T_2=373k$

$\Delta T=373-273=100k$

$\Delta v=\gamma v\Delta T$

Where v=Initial volume

$\Delta v$=Change in volume

Substitute the values then we get

$\Delta v=54\times 10^{-6}\times 1000\times 100=54\times 10^{-6}\times 100000=54\times 10^{-6}\times 10^5$

$\Delta v=5.4 cm^3$

$\Delta v=v_2-v_1$

$5.4=v_2-1000$

$v_2=5.4+1000=1005.4 cm^3$

Hence, the volume at 373 k=1005.4 cubic centimeter.

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