Question

Beryllium is used for making rocket parts because of its light weight and sturdiness. It also has a high specific heat that is second only to lithium among pure metals. This specific heat, which is 1825 J/kg•K, gives beryllium a high resistance to temperature change. Suppose a beryllium rocket component with a mass of 1.4 kg is tested at a high temperature and then cooled to 300.0 K. If the heat transferred away from the component is 2.555 x 106 J, what was the component's initial temperature?

Answer 1

The initial temperature of the beryllium rocket component was 1300.0 K, calculated using the formula for heat transfer in relation to the change in temperature.

Step-by-step explanation:

To find the initial temperature of the beryllium rocket component, we can use the formula relating heat transfer to change in temperature:

Q = mcΔT

where Q is the heat transferred, m is the mass, c is the specific heat capacity, and ΔT is the change in temperature (Tinitial - Tfinal). Given that the final temperature Tfinal is 300.0 K, the mass m is 1.4 kg, the specific heat c is 1825 J/kg•K, and the heat transferred away Q is 2.555 x 106 J, the formula can be rearranged to solve for the initial temperature:

Tinitial = (Q / (mc)) + Tfinal

Substituting the known values, we get:

Tinitial = (2.555 x 106 J / (1.4 kg × 1825 J/kg•K)) + 300.0 K

Tinitial = ((2.555 x 106 J / 2555 J/K) + 300.0 K

Tinitial = (1000 K) + 300.0 K

Tinitial = 1300.0 K

So, the initial temperature of the beryllium rocket component was 1300.0 K.