The temperatures of three Pyrex glass blocks are raised by the same amount. The

Question

The temperatures of three Pyrex glass blocks are raised by the same amount. The sizes (length x width x height) of the blocks are
block 1: 2D x 2D x D
block 2: D x D x 2D
block 3: 2D x D x 2D
with D = 5 cm.

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The temperatures of three Pyrex glass blocks are raised by the same amount. The sizes (length x width x height) of the blocks are
block 1: 2D x 2D x D
block 2: D x D x 2D
block 3: 2D x D x 2D
with D = 5 cm.

Explanation / Answer

(a) The change in height depends only on the height. This is so because on increasing the temperature every dimension (like height, width etc) increases proportional to original dimension.

(b) The change in height is proportional to the initial height. The initial height of block 1 is the smallest. So, block 1 has least change in height.

(c) Change in volume depends on initial volume. Since initial volume depends on height, width and length. So, change in volume depends on all these three dimensions (height, width and length).

(d) The change in volume is proportional to initial volume. Now, volumes of three blocks are:

V1 = 4D3, V2 = 2D3, V3 = 4D3.

So, the change in volume of block 2 is smallest.

(e) coefficient of linear expansion for pyrex glass is 4.0*10-6 K-1

So, change in height h1 of block 1 is = T h1 = 2*10-3 cm {since h1 = D = 5cm}

Similarly, h2 = 4*10-3 cm and h3 = 4*10-3 cm.

We can see that h1 is the smallest.

(f) We have, V = 3 T V

The factor of three comes in change in volume because all the three dimensions i.e. length, width and height increase by per meter per K.

Thus, V1 = 3*4.0*10-6*100*4D3 = 0.6 cm3

Similarly, V2 = 0.3 cm3 and V3 = 0.6 cm3

We can see that the change in volume is smallest in the case of block 2.

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