Determine the specific heat of a metal from the following data. A 75 g piece of the metal at 100.0 C was placed into an ice water bath. The heat loss from the metal melted 255g of ice. Some unmelted ice remained in the ice water bath.
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To determine the specific heat of the metal, we can use the formula:
Q = m * c * ΔT
where:
Q = heat lost or gained by the substance (in this case, metal)
m = mass of the substance (metal)
c = specific heat of the substance (metal)
ΔT = change in temperature
First, we need to calculate the heat lost by the metal. The heat lost by the metal will be equal to the heat gained by the ice, i.e., the heat required to melt the ice.
The heat required to melt the ice can be calculated using the formula:
Q = m * L
where:
Q = heat required
m = mass of the ice
L = latent heat of fusion of ice (334 J/g)
Given:
mass of ice (m) = 255 g
latent heat of fusion of ice (L) = 334 J/g
Substituting these values into the equation, we get:
Q = 255 g * 334 J/g
Q = 85,470 J
Now, we can find the specific heat (c) of the metal using the heat lost by the metal (Q), mass of the metal (m), and change in temperature (ΔT).
Given:
mass of metal (m) = 75 g
initial temperature of the metal (T1) = 100.0 °C
final temperature of the metal (T2) = the temperature of the ice water bath
Since we do not have the final temperature of the metal, we can assume it is the same as the final temperature of the ice water bath.
Substituting the values into the equation, we get:
Q = m * c * ΔT
85,470 J = 75 g * c * (0 - (0 - T2))
Since the initial and final temperature of the metal is the same, ΔT would be 0.
85,470 J = 75 g * c * 0
Now, we can solve for the specific heat (c).
c = 85,470 J / (75 g * 0)
c = 0 J/g°C
Therefore, the specific heat of the metal is 0 J/g°C.
To determine the specific heat of a metal, you need to use the formula:
q = m * c * ∆T
Where:
q = heat gained or lost
m = mass
c = specific heat
∆T = change in temperature
In this case, we are given the following information:
- The mass of the metal is 75 g.
- The initial temperature of the metal is 100.0°C.
- The heat loss from the metal melted 255 g of ice.
From the given data, we can start by finding the heat lost by the metal. To do this, we can use the formula for heat gained or lost by a substance:
q = m * c * ∆T
Since the metal is losing heat, we can use a negative value for q. Let's assume the final temperature of the metal after coming in contact with the ice water bath is 0°C. Therefore, the ∆T would be:
∆T = final temperature - initial temperature
∆T = 0°C - 100.0°C
∆T = -100.0°C
Now, we can use the mass and heat of fusion of ice to calculate the heat lost by the metal and used to melt the ice:
q = m * c * ∆T
q = (75 g) * c * (-100.0°C)
Next, let's calculate the heat required to melt the ice. The heat of fusion of ice is 333.5 J/g:
q = (255 g) * (333.5 J/g)
Finally, the total heat lost by the metal would be equal to the heat gained by the ice.
Therefore, we can set up the following equation:
(75 g) * c * (-100.0°C) = (255 g) * (333.5 J/g)
Now, we can solve this equation for the specific heat of the metal (c).