Question

A 3.00-m-long cylinder of solid aluminum has a radius of 2.00 cm.

1) If the cylinder is initially at a temperature of 3.00∘∘C, how much will the length change when the temperature rises to 30.0°C? (Express your answer to three significant figures.)

2) Due to the temperature increase, by how much (in %) would the density of the aluminum cylinder decrease? (Express your answer to three significant figures.)

3) By what percentage does the volume of the cylinder increase? (Express your answer to three significant figures.)

Answer 1

length,l=3m

radius, r=2cm

co-efficient of linear expansion, alpa=22.2*10^-6 /K

1)

T1=3 oC

T2=30 oC

change in dl=l1*alpa*dt

dl=3*22.2*10^-6*(30-3)

dl=0.001798 m

2)

co-efficient of volume expansion=3*alpa

change in volume, dV=V1*3*alpa*dT

percentage change in volume=(dV/v1)*100

=3*alpa*dT*100

=3*22.2*10^(-6)*(30-3)*100

=0.1798 %

and

mass, m=rho*V

==> percentage change in density, drho/rho=-(dV/v1)*100

= -0.1798 %

c)

percentage change in volume=(dV/v1)*100

= 0.1798 %