A non-isotropic solid metal cube has coefficients of linear expansion as: $5 \times 10^{-5} /{ }^{\circ} \mathrm{C}$ along the $\mathrm{x}=$ axis and $5 \times 10^{-6} /{ }^{\circ} \mathrm{C}$ along the y and the z -axis. If coefficient of volume expansion of the solid $\mathrm{C} \times 10^{-6} /{ }^{\circ} \mathrm{C}$ then the value of C is ____.

JEE Main · 2020 · 07 Jan 2020 · Shift 1 · Heat & Thermodynamics

A non-isotropic solid metal cube has coefficients of linear expansion as:

5 \times 1 0^{- 5} /^{\circ} C

along the

x =

axis and

5 \times 1 0^{- 6} /^{\circ} C

along the y and the z -axis. If coefficient of volume expansion of the solid

C \times 1 0^{- 6} /^{\circ} C

then the value of C is ____.

Answer: 60

Solution

For small expansions the volume coefficient is the sum of the three linear coefficients,

γ = α_{x} + α_{y} + α_{z}

. With

α_{x} = 5 \times 1 0^{- 5}

and

α_{y} = α_{z} = 5 \times 1 0^{- 6}

per

^{\circ} C

γ = 5 \times 1 0^{- 5} + 2 \times 5 \times 1 0^{- 6} = 60 \times 1 0^{- 6} /^{\circ} C

, so

C = 60

JEE Main · 2020 · 07 Jan 2020 · Shift 1 · Integer answer

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