Question

Water at room temperature of 20.0°C is poured into an aluminum cylinder which has graduation markings etched on the inside. The reading in the graduations is 300.0 cc. The cylinder with the water in it is then immersed in a constant temperature bath at a temperature of 100°C. What is the reading for the level of water on the graduations of the cylinder after the water and the cylinder reach thermal equilibrium with the bath? The volume coefficient of expansion of water is 2.07 × 10 -4 K -1, and the linear coefficient of expansion of aluminum is 23.0 × 10 -6 K -1. 305.0 cc 303.5 cc 304.5 cc 304.0 cc 303.3 cc

Answer 1

304.42 cc

Step-by-step explanation:

When the aluminum expands the markings will be further apart. If the 300 cc mark was at a distance l0 of the origin at 20 C, at 100 C it will be

l = l0 * (1 + a * (t - t0))

l = l0 * (1 + 23*10^-6 * (100 - 20))

l = l0 * 1.0018

The volume of water would have expanded by

V = V0 (1 + a * (t - t0))

V = 300 (1 + 2.07*10^-4 * (100 - 20))

V = 304.968 cc

Since the markings expanded they would measure

304.968/1.0018 = 304.42 cc