Math, asked by gaganSharma3134, 1 year ago

How to solve problems of volumetric expansion?

Answers

Answered by newnox40
1

Step-by-step explanation:

1. At 30 oC the volume of an aluminum sphere is 30 cm3. The coefficient of linear expansion is 24 x 10-6 oC-1. If the final volume is 30.5 cm3, what is the final temperature of the aluminum sphere?

Known :

The coefficient of linear expansion (α) = 24 x 10-6 oC-1

The coefficient of volume expansion (β) = 3 α = 3 x 24 x 10-6 oC-1 = 72 x 10-6 oC-1

The initial temperature (T1) = 30oC

The initial volume (V1) = 30 cm3

The final volume (V2) = 30.5 cm3

The change in volume (ΔV) = 30.5 cm3 – 30 cm3 = 0.5 cm3

Wanted : The final temperature (T2)

Solution :

ΔV = β (V1)(ΔT)

ΔV = β (V1)(T2 – T1)

0.5 cm3 = (72 x 10-6 oC-1)(30 cm3)(T2 – 30oC)

0.5 = (2160 x 10-6)(T2 – 30)

0.5 = (2.160 x 10-3)(T2 – 30)

0.5 = (2.160 x 10-3)(T2 – 30)

0.5 / (2.160 x 10-3) = T2 – 30

0.23 x 103 = T2 – 30

0.23 x 1000 = T2 – 30

230 = T2 – 30

230 + 30 = T2

T2 = 260oC

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