assume equal masses of the following substances, all of them at 20.0 degrees C and exposed to the same source of heat simultaneously. Which substance will reach a temp of 35.0 degress faster?

aluminium sp 0.900
lead sp 0.128
titanium sp 0.523
tin sp 0.222

and which one will take the longest time to heat up to 35.5 degrees C?

The long way is to make up a value for q and m and calculate delta T for each metal as in

q = m*c*delta T then choose the one that has the highest delta T value. The more esoteric way is to reason it out.
q = mcdelta T and solve for delta T.
dT = q/m*c
The problem says q is the same and m is the same so we have dT = k/c. That tells us that the lowest heat capacity will have the largest effect on dT. And the largest heat capacity will have the smallest effect on delta T. I like the esoteric way better.

lead

To determine which substance will reach a temperature of 35.0 degrees faster, we need to consider the specific heat capacity of each substance. Specific heat capacity (represented by the symbol "sp") is a measure of how much heat energy is required to raise the temperature of a given quantity of a substance.

The specific heat capacity tells us how much heat energy is needed to raise 1 gram of a substance by 1 degree Celsius. Therefore, a substance with a lower specific heat capacity requires less heat energy to raise its temperature compared to a substance with a higher specific heat capacity.

Given the specific heat capacities and assuming equal masses of the substances, we can compare their abilities to absorb heat and reach a temperature of 35.0 degrees faster:

- Aluminum (sp = 0.900): It has a relatively high specific heat capacity, meaning it requires a significant amount of heat energy to raise its temperature.

- Lead (sp = 0.128): Lead has the lowest specific heat capacity among the given substances, indicating that it requires less heat energy to increase its temperature compared to the others.

- Titanium (sp = 0.523): Titanium has a medium specific heat capacity, meaning it requires more heat energy to raise its temperature compared to lead but less than aluminum.

- Tin (sp = 0.222): Tin has a lower specific heat capacity compared to aluminum, indicating that it requires less heat energy to raise its temperature compared to aluminum but more than lead.

Based on the specific heat capacities, lead (sp = 0.128) will reach a temperature of 35.0 degrees faster compared to aluminum (sp = 0.900), titanium (sp = 0.523), and tin (sp = 0.222).