Question

A 23.0 g copper ring at 0.000°C has an inner diameter of
*D* = 2.46000 cm. An aluminum sphere at 100.0°C has a
diameter of *d* = 2.46507 cm. The sphere is put on top of
the ring, and the two are allowed to come to thermal equilibrium,
with no heat lost to the surroundings. The sphere just passes
through the ring at equilibrium temperature.

What is the mass of the sphere?

Answer #1

Let T be the equilibrium temperature when sphere passes through the ring and their equal diameters be k.

Using coefficients of expansion of Copper and Aluminum

The linear expansion equation is: ΔL=αLiΔT where ΔL = Lf - Li

For Cu

{(k - 2.46)/2.46} = 0.000017 x T

For Al

{(2.46507 - k) / 2.46507} = 0.000023 x T

From above two equation

(2.46507 -2.46)/2.4625 = Tx(0.000040) or

T = 0.00508/(2.5425*0.000040) = 51.47 degree Celsius

Since it's in thermal equilibrium the sume of their heat energy (Q)
will equal 0.

Qcu + Qal= 0

Q=mcΔT.

(51.47-0) x 23x0.835 = M*(100-51.47)x0.385

M = (0.835/0.385)*20 g = **52.905 g**

A 23.0 g copper ring at 0.000°C has an inner diameter of
D = 2.46000 cm. An aluminum sphere at 100.0°C has a
diameter of d = 2.46507 cm. The sphere is put on top of
the ring, and the two are allowed to come to thermal equilibrium,
with no heat lost to the surroundings. The sphere just passes
through the ring at equilibrium temperature.
What is the mass of the sphere?

At 20∘C, the hole in an aluminum ring is 2.100 cm in diameter.
You need to slip this ring over a steel shaft that has a
room-temperature diameter of 2.107 cm To what common temperature
should the ring and the shaft be heated so that the ring will just
fit onto the shaft? Coefficients of linear thermal expansion of
steel and aluminum are 12×10−6 K−1 and 23×10−6 K−1
respectively.

At 20∘C, the hole in an aluminum ring is 2.200 cm in diameter.
You need to slip this ring over a steel shaft that has a
room-temperature diameter of 2.204 cm .
To what common temperature should the ring and the shaft be
heated so that the ring will just fit onto the shaft? Coefficients
of linear thermal expansion of steel and aluminum are
12×10-6K-1 and
23×10-6K-1 respectively.
Express your answer in degrees Celsius to two significant
figures.

A hot lump of 46.2 g of copper at an initial temperature of 93.9
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A hot lump of 27.5 g of copper at an initial temperature of 54.7
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To what temperature, in degrees Celsius, must the rod and ring
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