A solid steel cube is stored in a freezer, where the temperature is -20.0 °C. While thecube is in the freezer, you measure its side length (L) to be 1.75050 meters. The cube isthen placed outside for a long time, so that the temperature of the cube reaches thetemperature of the air outside. As a result, the side length increases to 1.75170 meters dueto thermal expansion. The coefficient of linear expansion for steel is 12.0×10-6 °C-1.(a) What is the temperature of the air outside? Give youranswer in degrees Celsius ('C).(b) What is the volume of the cube when its temperature is 20.0 °C? Give youranswer in cubic meters (m3).

(a) Using linear thermal expansion Lf-LiLi=αLTf-TiTf=Lf-LiαLLi+Ti=1.75170 m-1.75050 m12.0×10-6 /°C1.75050 m+-20.0 °C=37.126 °C≈37.1 °C(b) Volume of the cube at 20.0°C Vf=Li+ΔL3=Li+LiαLTf-Ti3=1.75050 m+1.75050 m12.0×10-6 /°C20° C--20.0 °C3=5.371697 m3≈5.37 m3

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