To determine which substance has the higher specific heat, we need to consider the amount of energy required to raise the temperature of each substance by 1 degree Celsius.
The specific heat is defined as the amount of heat energy required to raise the temperature of one gram of a substance by 1 degree Celsius. A substance with a higher specific heat requires more heat energy to raise its temperature than a substance with a lower specific heat.
When the metal at 100°C is dropped into the water at 20°C, heat energy flows from the metal to the water until they reach a common final temperature of 35°C. The heat released by the metal is equal to the heat absorbed by the water, according to the law of conservation of energy:
m * c * ΔT = Q
where:
m is the mass of the substance
c is the specific heat of the substance
ΔT is the change in temperature
Q is the amount of heat energy transferred
We can calculate the amount of heat released by the metal using:
Q = m * c * ΔT
For the metal, m = 10 g, ΔT = (35°C - 100°C) = -65°C, and Q is negative since heat is being released:
Q = 10 g * c * (-65°C)
We can also calculate the amount of heat absorbed by the water using:
Q = m * c * ΔT
For the water, m = 10 g, ΔT = (35°C - 20°C) = 15°C, and Q is positive since heat is being absorbed:
Q = 10 g * c * (15°C)
Setting these two equations equal to each other and solving for c, we get:
10 g * c * (-65°C) = 10 g * c * (15°C)
-65°C = 15°C
This equation cannot be true, which means that there must be an error somewhere in our calculations. The error comes from assuming that the heat capacity of the two substances is equal, which is incorrect. In reality, metals typically have much lower specific heats than water. Therefore, the substance with the higher specific heat is water.