Consider the following metals.
Metal
Specific Heat
copper
0.385 J/(g · °C)
magnesium
1.02 J/(g · °C)
mercury
0.138 J/(g · °C)
silver
0.237 J/(g · °C)
lead
0.129 J/(g · °C)
If the same amount of heat is added to 25.0 g of each of the metals, which are all at the same initial temperature, which metal will have the highest final temperature?
Silver
wrong
To determine which metal will have the highest final temperature, we need to compare their specific heat capacities. The metal with the lowest specific heat capacity will experience the highest increase in temperature when the same amount of heat is added.
Let's calculate the amount of heat (q) using the formula:
q = m × c × ΔT
where:
q represents the heat,
m is the mass of the metal (25.0 g for each),
c is the specific heat capacity of the metal, and
ΔT is the change in temperature.
Since the initial temperature is the same for all metals, the change in temperature can be ignored.
For copper:
q = (25.0 g) × (0.385 J/(g·°C)) = 9.625 J
For magnesium:
q = (25.0 g) × (1.02 J/(g·°C)) = 25.5 J
For mercury:
q = (25.0 g) × (0.138 J/(g·°C)) = 3.45 J
For silver:
q = (25.0 g) × (0.237 J/(g·°C)) = 5.925 J
For lead:
q = (25.0 g) × (0.129 J/(g·°C)) = 3.225 J
Now, let's compare the values of q. The metal with the highest value of q will have the highest final temperature since the same amount of heat is added to each metal.
Calculating the values of q:
Copper: q = 9.625 J
Magnesium: q = 25.5 J
Mercury: q = 3.45 J
Silver: q = 5.925 J
Lead: q = 3.225 J
Based on the values, magnesium will have the highest final temperature since it requires the most heat (25.5 J) to reach the same change in temperature as the other metals.
To determine which metal will have the highest final temperature when the same amount of heat is added to each metal, we need to use the heat equation:
Heat (Q) = mass (m) x specific heat (c) x change in temperature (ΔT)
Since the mass and initial temperature are the same for all metals in this scenario, we can ignore them and focus on the specific heat and change in temperature.
The equation can be rearranged to solve for the change in temperature:
ΔT = Q / (m x c)
Substituting the values given for each metal into the equation:
For copper:
ΔT = Q / (m x c) = Q / (25.0 g x 0.385 J/(g · °C))
For magnesium:
ΔT = Q / (m x c) = Q / (25.0 g x 1.02 J/(g · °C))
For mercury:
ΔT = Q / (m x c) = Q / (25.0 g x 0.138 J/(g · °C))
For silver:
ΔT = Q / (m x c) = Q / (25.0 g x 0.237 J/(g · °C))
For lead:
ΔT = Q / (m x c) = Q / (25.0 g x 0.129 J/(g · °C))
Now, in all cases, the same amount of heat (Q) has been added to each metal. Therefore, the metal that will have the highest final temperature is the metal with the lowest specific heat value, as a lower specific heat means that it requires less heat energy to increase the temperature.
From the given data, we can see that lead has the lowest specific heat (0.129 J/(g · °C)). Therefore, lead will have the highest final temperature when the same amount of heat is added to each metal.