Two metals P and Q of length l1 and l2 are heated through the same temperature difference. If the ratio of the linear expansivities of P to Q is 2:3 and the ratio of lengths is 3:4. What is the ratio of increase in length of P to Q?
Metals P, Q
original length lP, lQ
Increase in length ΔlP, ΔlQ
Linear expansivities αP, αQ
∴ αP/αQ = 2/3 ; and lP/lQ = 3/4
But increase in length, Δl = αlΔθ
∴ΔlP = αPlPΔθ
ΔlQ = αQlQΔθ
| ∴ | ΔlP | = | αPlPΔθ | = | 2 | x | 3 | = | 1 |
| ΔlQ | αQlQΔθ | 3 | 4 | 2 |
∴ Ratio of increase in length of P to Q = 1:2
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