Thermal coefficients of expansion

AI Thread Summary
The discussion revolves around calculating the temperature change required to close the gap between a brass rod and a copper sheet with a specific hole size. The initial equation presented for linear expansion is deemed incorrect, and the correct formula is suggested as L = L0(1 + αΔT). Participants express confusion regarding the formula and its components, particularly the meaning of L. Clarification is sought on how to apply the formula to determine the new dimensions of both the rod and the hole after a temperature change. Understanding thermal expansion concepts is emphasized as crucial for solving the problem.
Brian13
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Homework Statement


A brass rod (linear expansion coef 19*10-6/°C) has a radius of 8139 cm and a copper (linear expansion coef 17*10-6/°C) sheet has a hole or radius 8139+8.86cm. What temperature change (K) is required to close the gap?

Homework Equations


ΔL/Lo = αΔT?

The Attempt at a Solution


I'm not even sure if the equation is right, so I'm really confused. Thanks for the help!
 
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Brian13 said:

Homework Statement


A brass rod (linear expansion coef 19*10-6/°C) has a radius of 8139 cm and a copper (linear expansion coef 17*10-6/°C) sheet has a hole or radius 8139+8.86cm. What temperature change (K) is required to close the gap?

Homework Equations


ΔL/Lo = αΔT?

The Attempt at a Solution


I'm not even sure if the equation is right, so I'm really confused. Thanks for the help!
That's some rod, if it has a diameter of over 16 meters!

Are you certain these are the dimensions for this problem?
 
I'm positive!
 
The equation is not correct. It should be:
$$L=L_0(1+\alpha \Delta T)$$So, if the temperature rises ΔT, in terms of #\Delta T#, what it the new radius of the rod? What is the new radius of the hole in the sheet?
 
I'm not entirely sure. I don't really understand the formula, so I'm having a hard time really wrapping my mind around it. I don't know what the L represents.
 
Brian13 said:
I'm not entirely sure. I don't really understand the formula, so I'm having a hard time really wrapping my mind around it. I don't know what the L represents.
Please say in words your understanding of the concept of thermal expansion.

Chet
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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