Explanation When the volume of anything is increased or decreased, volume expansion is applied. Coefficient of volume expansion for coolant is much larger than of aluminium radiator and steel engine, so coolant will expand more than aluminium and steel and it will overflow the system. Write the expression for volume expansion of the substance. Δ V = β V o Δ T (I) Here, Δ V is change in volume, β is coefficient of volume expansion, V o is original volume at initial temperature and Δ T is the change in temperature. Assume β C for coefficient of volume expansion for coolant, β A for coefficient of volume expansion for aluminum, β S for coefficient of volume expansion for steel. Also assume V C for volume of Coolant, V A for volume of aluminum radiator and V S for Volume of steel engine. Write the expression for net change in volume which is also the amount overflowing to the reservoir. Δ V = Δ V C − Δ V A − Δ V S Substitute β C V C Δ T for Δ V C , β A V A Δ T for Δ V A and β S V S Δ T for Δ V S in above equation. Δ V = β C V C Δ T − β A V A Δ T − β S V S Δ T Simplify above equation. Δ V = ( β C V C − β A V A − β S V S ) Δ T (II) Write the expression for Δ T . Δ T = T − T o Here, T o is the initial temperature and T is the is increased temperature. Substitute T − T o for Δ T in equation (II)

Physics for Scientists and Engineers with Modern Physics

4th Edition

ISBN: 9780136139225

Author: Douglas C. Giancoli

Publisher: Prentice Hall

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Chapter 17, Problem 16P

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Physics for Scientists and Engineers with Modern Physics

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