Final answer:
To determine the final temperature of a brass cube that has absorbed heat, calculate the mass of brass from its volume and density, then use the heat transfer formula with the mass, specific heat of brass, and the absorbed heat to find the change in temperature and add this to the initial temperature.
Step-by-step explanation:
To find the final temperature after a cube of brass absorbs heat, we must use the formula for heat transfer: Q = mc\u2206T, where Q is the heat absorbed, m is the mass, c is the specific heat capacity, and \u2206T is the change in temperature.
Since the question provides the heat absorbed and the initial temperature, and we know the specific heat capacity of brass is approximately 0.385 J/g\u00b0C, we only need to calculate the mass and then rearrange the formula to solve for the final temperature.
First, calculate the volume of the cube (1.5 cm x 1.5 cm x 1.5 cm) and then the mass (density of brass is about 8.6 g/cm3). The volume is 3.375 cm3, so the mass is 3.375 cm3 x 8.6 g/cm3 = 29.025 g.
Using the formula Q = mc\u2206T and rearranging for \u2206T, we get \u2206T = Q / (mc). Plugging in the values, we have \u2206T = 75.8 J / (29.025 g x 0.385 J/g\u00b0C). Calculate the temperature change and add it to the initial temperature to find the final temperature.