Question

A steel ring with a hole having area of 3.99 cm² is to be placed on an aluminum rod with cross- sectional area of 4.00 cm². Both rod and ring are initially at a temperature of 35.0 °C. At what common temperature can the steel ring be slipped onto one end of the aluminum rod? ​

Answer 1

The common temperature at which the steel ring can be slipped onto one end of the aluminum rod is 33.0°C. This is because the expansion of both materials due to the temperature rise need to be balanced for the steel ring to fit on the aluminum rod. The equation for this is A1T2 = A2T1, where A1 and A2 are the areas of the steel ring's hole and the aluminum rod, respectively, and T1 and T2 are the initial and the common temperatures. Solving this equation yields T2 = 33.0°C.

Answer 2

To find the common temperature at which the steel ring can be slipped onto the aluminum rod, calculate the heat conduction rates through each material using the formula Heat Conduction Rate = Thermal Conductivity x Cross-sectional Area x Temperature Difference / Length. Set the two heat conduction rates equal to each other and solve for the common temperature.

Step-by-step explanation:

In order to find the common temperature at which the steel ring can be slipped onto the aluminum rod, we need to consider the heat conduction between the two materials. The rate of heat conduction through each material can be calculated using the formula:

Heat Conduction Rate = Thermal Conductivity x Cross-sectional Area x Temperature Difference / Length

By setting the two heat conduction rates equal to each other and solving for the common temperature, we can find the answer.