Passage VII

Introduction

Two solid metal cylinders (X and Y) have the same length and cross-sectional area. Cylinder X is made of hypothetical Metal X, and Cylinder Y is made of hypothetical Metal Y.

Both cylinders are at 25°C. The exterior of each cylinder is insulated everywhere except at one end. Two students are asked the following question: If the 2 cylinders are dropped into a container of boiling water at the same time, the insulated end of which cylinder will reach 50°C first?

Relevant physical properties for Cylinder X and Metal X are listed in Tables 1 and 2, respectively. The value of each physical property for Cylinder X (Metal X) is expressed as a multiple of the value of the same physical property for Cylinder Y (Metal Y).

Each student proposed a different answer to the question they were asked.

Student 1

Because TC of Metal X is 2 times that of Metal Y and the cylinders are the same size, the rate of heat conduction within Cylinder X will be 2 times that within Cylinder Y. Therefore, the rate at which heat flows into Cylinder X will be 2 times the rate at which heat flows into Cylinder Y, and the insulated end of Cylinder X will take half as long as the insulated end of Cylinder Y to reach 50°C.

Student 2

The heat capacity (HC) of each cylinder equals SH of the metal times the mass of the cylinder, so HC of Cylinder X is 4 times HC of Cylinder Y. Thus, to reach 50℃, the insulated end of Cylinder X must absorb 4 times as much heat as the insulated end of Cylinder Y. Because the rate at which heat flows into Cylinder X will be only 2 times that for Cylinder Y, the insulated end of Cylinder X will take 2 times as long to reach 50°C as the insulated end of Cylinder Y.