Thermal expansion of floating cylinder · CAP 2015 #5

Physics · thermodynamics

Problem

As shown in the picture a cylinder with volumetric thermal expansion coefficient of

\beta_c = 3 \times 10^{-6}/^\circ

C is completely submerged and floating in a fluid at the temperature

50^\circ

C. The fluid has volumetric thermal expansion coefficient of

\beta_f = 8 \times 10^{-5}/^\circ

C. If we cool down the cylinder and the fluid to

0^\circ

C what percentage of the cylinder's height will be out of the fluid? a) 0.39% b) 0.42% c) 0.78% d) 0.84%