Question

The marking of an aluminium ruler and brass rulerare perfectly aligned at 0 degrees Celsius. How far apart willthe 20.0cm marks be on the two rulers at 100 degrees Celsius. If precise alignment of the left hand ends of the rulers is maintained.

Answer 1

Answer;

Difference in the length of two scales is given as

L_{Al} - L_{brass} = 0.013 cmL

Al

−L

brass

=0.013cm

Explanation:

As we know that if temperature of the solid rod is increased then due to thermal expansion its length will increase

Here we know that the coefficient of thermal expansion is given as

\alpha_{brass} = 19 \times 10^{-6}α

brass

=19×10

−6

the coefficient of thermal expansion is given as

\alpha_{Al} = 24 \times 10^{-6}α

Al

=24×10

−6

Now final length of 25 cm mark for both scale is given as

L_{Al} = 25(1 + (24 \times 10^{-6})(104.7 - 0))L

Al

=25(1+(24×10

−6

)(104.7−0))

L_{brass} = 25(1 + (19 \times 10^{-6})(104.7 - 0))L

brass

=25(1+(19×10

−6

)(104.7−0))

now difference in length is given as

L_{Al} - L_{brass} = 25(104.7)(24 \times 10^{-6} - 19\times 10^{-6})L

Al

−L

brass

=25(104.7)(24×10

−6

−19×10

−6

)

L_{Al} - L_{brass} = 0.013 cmL

Al

−L

brass

=0.013cm

#Learn

Topic : thermal Expansion