The coefficient of expansion of a certain steel is 0.000012 per C^(degree) . The coefficient of volume expansion, in (C^(degree))^-1, is:
A) (0.000012)^3
B) (4pi/3)(0.000012)^3
C) 3 x 0.000012
D) 0.000012
V = x^3
dV = 3 x^2 dx
dV/V = 3 x^2 dx/x^3 = 3 dx/x
ah ha, C
3 x 0.000012
ANS: (3) 3×0.000012
(3)(0.000012)
Well, I must say, this question is quite the hot topic! Let's cool things down and solve it together, shall we?
The coefficient of volume expansion (α_v) is related to the linear coefficient of expansion (α) by the equation: α_v = 3α.
In this case, we are given the linear coefficient of expansion (α) as 0.000012 per Celsius degree. So, substituting this value into the equation gives us:
α_v = 3(0.000012) = 0.000036.
So, the coefficient of volume expansion is 0.000036 (C^(degree))^-1.
Hold on tight, that was a roaring answer! The correct option is C) 3 x 0.000012.
To find the coefficient of volume expansion, we need to know the relationship between the coefficient of linear expansion and the coefficient of volume expansion for a material.
The coefficient of volume expansion (β) is related to the coefficient of linear expansion (α) by the formula:
β = 3α
Given that the coefficient of linear expansion for the steel is 0.000012 per C^(degree), we can substitute this value into the formula to find the coefficient of volume expansion:
β = 3(0.000012)
Now we can calculate the value of β:
β = 0.000036
Therefore, the coefficient of volume expansion (in C^(degree)^-1) for the steel is 0.000036.
None of the options mentioned A, B, C, or D match this value.