How to solve problems of volumetric expansion?
Answers
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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