Question

An aluminum rod is 116.5 cm long at 20.0 degrees Celsius and has a mass of 450g. If 120,000 J of energy is added to the rod by heat, What is the change in the length of the rod?

Answer 1

initial length of the rod l1=116.5 cm

initial temperature T1=20 oC

mass of the aluminum rod, m=450g

heat enegry added Q=120000 J

coefficient of linear expansion of aluminum, alpa=2.22*10-5 /oC

specific heat capacity of Aluminum, C_Alu=900 J/kg*oC

use,

heat enegry,

Q=m*C_Alu*(T2-T1)

120000=450*10^-3*(900)*(T2-20)

====> T2=316.3 oC

after heating, final temperature of the rod T2=316.3 oC

now,

change length of the rod, dl=l1*alpa*(T2-T1)

dl=(116.5cm)*(2.22*10^-5)*(316.3-20)

dl=0.77cm

change in length dl=0.77cm