Question

A brass rod is .500 m long at 20.0 degree C. What is the length of the rod if it is heated to 50.0 degree C?

Answer 1

Solution:

Length of Brass Rod , $l_{Br_{1} }$ = 0.500 m

Initial Temperature , t₁ = 20°C

Final Temperature , t₂ = 50°C

Coefficient of linear expansion for Brass , $\alpha_{Br}$ = 19 * 10⁻⁶ /°C

Length of Brass Rod after heating , $l_{Br_{2} }$ = ?

$l_{Br_{2} } = l_{Br_{1} } [ 1 + \alpha_{Br} ( t_{2} - t_{1} ) ]$

$l_{Br_{2} } = 0.500 [ 1 + 19 * 10^{-6} ( 50 - 20 ) ]$

$l_{Br_{2} } = 0.500 [ 1 + 19 * 10^{-6} * 30 ]$

$l_{Br_{2} } = 0.500 [ 1 + 570 * 10^{-6}]$

$l_{Br_{2} } = \frac{500}{1000} [ 1 + 570 * 10^{-6}]$

$l_{Br_{2} } = \frac{1}{2} [ 1 + 570 * 10^{-6}]$

$l_{Br_{2} } = \frac{1}{2} [ 1 + 0.00057]$

$l_{Br_{2} } = \frac{1.00057}{2}$

$l_{Br_{2} } = 0.500285\ m$

The length of the brass rod after heating will be 0.500285 m

Answer 2

Thus the length of the rod is lBr2 =  0.500285 m

Explanation:

• Length of Brass Rod,  = 0.500 m
• Initial Temperature, t₁ = 20°C
• Final Temperature, t₂ = 50°C
• Coefficient of linear expansion for Brass,  = 19 x 10⁻⁶ /°C

Solution:

Length of Brass Rod after heating lBr2 = ?

lBr2 = lBr1 [1 + αBr2 ( t2 - t1)]

lBr2 =  0.500 [ 1 + 19 x 10^-6 (50 - 20 )]

lBr2 = 0.500 [ 1 + 570 x 10^-6]

lBr2 =  500 / 1000 [ 1 + 570 x 10^6]

lBr2 =  1 / 2 [ 1 + 570 x 10^-6]

lBr2 =  1/2 [ 1 + 0.00057]

lBr2 =  1.00057 / 2

lBr2 =  0.500285 m

Thus the length of the rod is lBr2 =  0.500285 m