Final answer:
To find the initial temperature of the aluminum sample, we can use the principle of heat transfer and set up equations for the heat lost by the copper and heat gained by the aluminum. By solving these equations, we can calculate the initial temperature of the aluminum sample.
Step-by-step explanation:
To solve this problem, we need to apply the principle of heat transfer, which states that the heat gained by one object is equal to the heat lost by another object in thermal contact. We can use the formula:
q = m * c * ΔT
where q is the heat gained or lost, m is the mass, c is the specific heat, and ΔT is the change in temperature.
We are given the masses, initial temperatures, and final temperatures of the aluminum and copper samples. By setting up two equations, one for heat lost by copper and one for heat gained by aluminum, we can solve for the initial temperature of aluminum.
Let's use the equation for heat lost by copper:
q(copper) = m(copper) * c(copper) * (T(final) - T(initial))
Substituting the given values and rearranging the equation, we find:
T(initial) = T(final) - (m(copper) * c(copper) * (T(final) - T(aluminum))/ (m(aluminum) * c(aluminum)))
Plugging in the values, we can calculate the initial temperature of the aluminum sample.