Thermal expansion causes most solids to increase in length. If the increase is l

Question

Thermal expansion causes most solids to increase in length. If the increase is linear with temperature and such that the length increases by 0.1% for each 100 degree C,

a.)calculate in m^3 the change in volume that a 30 ft diameter sphere will experience when the temperature is increased 100degreeC.

b.)same as (a) but expressing the change in %.

c.) if the sphere is solid and has an initial density of 2 g/cm^3, calculate the final density when the temperature is increased 100degreeC.

d.)same as (b) but for a cube 30ft on the side

Explanation / Answer

l = lT

l/l x 100 = .1 for T=100

T = .001

a)

R/R = T

change in volume V = V * 3R/R =42.4 ft3 =12.92 m3

b)

V/V * 100 = 3*.1 = .3 %

c)

volume is inversely proportional to density so

V/V = - /

1 - 2 = .003*2 = .006

2 = 1.994 g/cm3

d)

V/V * 100 = 3 a/a *100 = 3* .001*100

= .3%

 

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