The linear expansivity of a metal P is twice that of another metal Q. When these materials are heated through the same temperature change, their increase in...
Question 1 Report
The linear expansivity of a metal P is twice that of another metal Q. When these materials are heated through the same temperature change, their increase in length is the same. Calculate the ratio of the original length of P to that of Q.
Answer Details
Let the original length of metal P be x and the original length of metal Q be y. We know that the increase in length is given by: ΔL = L₀αΔθ where ΔL is the increase in length, L₀ is the original length, α is the coefficient of linear expansion, and Δθ is the change in temperature. Since the increase in length is the same for both metals, we can write: ΔLP = ΔLQ LPαPΔθ = LQαQΔθ LP/LQ = αQ/αP Since we are told that the linear expansivity of P is twice that of Q, we can write: αP = 2αQ Substituting into the equation above, we get: LP/LQ = αQ/2αQ = 1/2 Therefore, the ratio of the original length of P to that of Q is 1:2. Answer: 1:2
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