How me how to calculate
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.
if P and Q have the same length increase
then P must originally be half the length of Q
... because its linear expansivity is twice that of Q
q
Pls can u give the workings
Pls can u give the workings
Physics
Please can you show the workings
Pls can you show the workings
Pls show solvings
To calculate the ratio of the original length of metal P to metal Q, we need to consider the linear expansivity of the metals and the increase in length when they are heated through the same temperature change.
Let's denote the linear expansivity of metal P as αP and the linear expansivity of metal Q as αQ. We are given that αP is twice that of αQ.
The linear expansivity (α) of a material describes how much it expands per unit length when heated by one degree of temperature change. It is usually given in units of 1/°C.
Let's suppose the original lengths of metal P and metal Q are LP and LQ, respectively.
When they are heated through the same temperature change, the increase in length of metal P is ΔLP and the increase in length of metal Q is ΔLQ. We are given that ΔLP = ΔLQ.
The formula to calculate the increase in length of a material is given by:
ΔL = α * L * ΔT
Where:
ΔL is the increase in length,
α is the linear expansivity of the material,
L is the original length of the material, and
ΔT is the temperature change.
Since both metals are heated through the same temperature change, ΔT is the same for both ΔLP and ΔLQ.
Now, let's solve for the ratio of the original lengths of P to Q.
For metal P:
ΔLP = αP * LP * ΔT
For metal Q:
ΔLQ = αQ * LQ * ΔT
Since ΔLP = ΔLQ, we can equate the two equations:
αP * LP * ΔT = αQ * LQ * ΔT
Dividing both sides of the equation by ΔT yields:
αP * LP = αQ * LQ
Given that αP = 2αQ, we can substitute this into the equation:
2αQ * LP = αQ * LQ
Now, we can cancel out the αQ terms:
2LP = LQ
Finally, dividing both sides of the equation by LQ gives us the ratio of the original length of P to Q:
LP/LQ = 1/2
So, the ratio of the original length of metal P to that of metal Q is 1:2.