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A non-isotropic solid metal cube has coefficients of linear expansion as 5 × 10-5/°C along the x-axis and 5 × 10-6/°C along the y and the z-axis. If the coefficient of volume expansion of the solid is C × 10-6/°C, then the value of C is
Correct answer is '60'. Can you explain this answer?
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A non-isotropic solid metal cube has coefficients of linear expansion ...
As it is a cube, so all its sides are equal. Let the length of cube be L.
Given, αx = 5 × 10-5/°C and = αy = 5 × 10-6/°C = αz
Let the coefficient of volume expansion be γ.
After increase in temperature, increase in volume of cube = L3 × γ ..... (1)
Or, increase in volume of cube = L3(1 + αx)(1 + αy)(1 + αz) ..... (2)
From equations (1) and (2), we get
γL3 = L3(1 + αx)(1 + αy)(1 + αz)
⇒ γ = (5 × 10-5 + 5 × 10-6 + 5 × 10-6)
⇒ γ = 6 × 10-5/°C
From question,
γ = C × 10-6/°C
So, C = 60
Given, αx = 5 × 10-5/°C and = αy = 5 × 10-6/°C = αz
Let the coefficient of volume expansion be γ.
After increase in temperature, increase in volume of cube = L3 × γ ..... (1)
Or, increase in volume of cube = L3(1 + αx)(1 + αy)(1 + αz) ..... (2)
From equations (1) and (2), we get
γL3 = L3(1 + αx)(1 + αy)(1 + αz)
⇒ γ = (5 × 10-5 + 5 × 10-6 + 5 × 10-6)
⇒ γ = 6 × 10-5/°C
From question,
γ = C × 10-6/°C
So, C = 60
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A non-isotropic solid metal cube has coefficients of linear expansion as 5 × 10-5/°C along the x-axis and 5 × 10-6/°C along the y and the z-axis. If the coefficient of volume expansion of the solid is C × 10-6/°C, then the value of C isCorrect answer is '60'. Can you explain this answer?
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