Two rods of different materials having coefficients of thermal expansion α$$1$$ and α$$2$$ and Young's moduli $$Y1$$ and $$Y2$$ are fixed between two rigid and massive walls. The rods are heated to the same temperature. If there is no bending of the rods, the thermal stresses developed in them are equal provided

Question

Two rods of different materials having coefficients of thermal expansion α$$1$$ and α$$2$$ and Young's moduli $$Y1$$ and $$Y2$$ are fixed between two rigid and massive walls. The rods are heated to the same temperature. If there is no bending of the rods, the thermal stresses developed in them are equal provided

Infinity Learn · Accepted Answer

When a rod is heated to a temperature T, the increase in its length l is given by $$I=$$α LTwhere l, $$=$$ $$len8th$$ of the rodand α$$=coefficient$$ of thermal expansion∴  strain $$=lL=$$αTand stress $$=$$ Y x strain $$=$$ YαTSince the value of T is same for the two rods and hence the stresses in them will be equal $$ifY1$$α$$1T=Y2$$α$$2T$$  or  $$Y1Y2=$$α$$2$$α$$1$$

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Two rods of different materials having coefficients of thermal expansion α1 and α2 and Young's moduli Y1 and Y2 are fixed between two rigid and massive walls. The rods are heated to the same temperature. If there is no bending of the rods, the thermal stresses developed in them are equal provided

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