A thin brass sheet at $$10$$°C and a thin steel sheet at $$20$$°C have the same surface area. The common temperature at which both would have the same area is (coefficient$$ of linear expansion for brass and steel are $$19$$ x $$10-6/$$°C and $$11$$ x $$10-6/$$°C $$respectively)

Question

A thin brass sheet at $$10$$°C and a thin steel sheet at $$20$$°C have the same surface area. The common temperature at which both would have the same area is (coefficient$$ of linear expansion for brass and steel are $$19$$ x $$10-6/$$°C and $$11$$ x $$10-6/$$°C $$respectively)

Infinity Learn · Accepted Answer

The area of brass sheet at $$10$$°C $$=$$ $$a1$$ $$b1Area$$ of steel sheet at $$20$$°C $$=$$ $$a2$$ $$b2Given$$ that    $$a1b1=a2b2$$           ....$$(1)Let$$ the common temperature be T. Then at temperature T, the lengths of the two sheets are $$respectivelya11+$$αBT  and  $$a21+$$αSTNow,  $$a11+$$αBT×$$b11+$$αBT            $$=a21+$$αST×$$b21+$$αSTor   $$1+$$α$$BT2=1+$$α$$ST2$$ ∵$$a1b1=a2b2Substituting$$ the values of αB and αS and solving we $$getT=$$−$$3$$⋅$$75$$∘C

A thin brass sheet at 10°C and a thin steel sheet at 20°C have the same surface area. The common temperature at which both would have the same area is (coefficient of linear expansion for brass and steel are 19 x 10^-6/°C and 11 x 10^-6/°C respectively)

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A thin brass sheet at 10°C and a thin steel sheet at 20°C have the same surface area. The common temperature at which both would have the same area is (coefficient of linear expansion for brass and steel are 19 x 10-6/°C and 11 x 10-6/°C respectively)

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Ready to Test Your Skills?

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A thin brass sheet at 10°C and a thin steel sheet at 20°C have the same surface area. The common temperature at which both would have the same area is (coefficient of linear expansion for brass and steel are 19 x 10^-6/°C and 11 x 10^-6/°C respectively)