Question

Calculate the linear expansivity or brass or length 170m,that assumes new length of 120.05m when heated through the temperature of 100⁰c

Calculate also the area and heated expansivity

Answer 1

Solution.

$L_0=120m;$

$L=120.05m;$

$\Delta T=100^OC=100K;$

$L=L_0(1+\alpha_L t)\implies \alpha_L=\dfrac{L-L_0}{L_0\Delta T};$

$\alpha_L=\dfrac{120.05-120}{120\sdot100}=4.2\sdot 10^{-6}K^{-1};$

$\alpha_A=2\alpha_L;$

$\alpha_A=2\sdot4.2\sdot10^{-6}=8.4\sdot10^{-6}K^{-1};$

$\alpha_V=3\alpha_L;$

$\alpha_V=3\sdot4.2\sdot10^{-6}=12.6\sdot10^{-6}K^{-1};$

Answer: $\alpha_L=4.2\sdot 10^{-6}K^{-1};$

$\alpha_A=8.4\sdot10^{-6}K^{-1};$

$\alpha_V=12.6\sdot10^{-6}K^{-1}.$