Exactly 10.0 mL of water at 25.0 °C is added to a hot iron skillet. All of the water is converted to steam at 100.0°C. The mass of the skillet is 1.45 kg. What is the change in temperature of the skillet?
To find the change in temperature of the skillet, we need to calculate the heat transferred from the skillet to the water.
First, let's calculate the heat required to convert 10.0 mL of water at 25.0 °C into steam at 100.0 °C. We can use the formula:
Q = m * c * ΔT
Where:
Q is the heat transferred
m is the mass of the water
c is the specific heat capacity of water
ΔT is the change in temperature
The mass of the water can be calculated using its density (which is approximately 1.0 g/mL):
mass = volume * density
mass = 10.0 mL * 1.0 g/mL = 10.0 g
The specific heat capacity of water is approximately 4.18 J/g·°C.
Now, let's calculate the heat transferred:
Q = 10.0 g * 4.18 J/g·°C * (100.0 °C - 25.0 °C)
Q = 10.0 g * 4.18 J/g·°C * 75.0 °C
Q = 3135 J
So, the heat transferred from the skillet to the water is 3135 J.
Now, to find the change in temperature of the skillet, we can use the formula:
Q = m * c * ΔT
Where:
Q is the heat transferred (3135 J)
m is the mass of the skillet (1.45 kg)
c is the specific heat capacity of iron (approximately 450 J/kg·°C, varies slightly depending on the type of iron used)
ΔT is the change in temperature of the skillet (what we are solving for)
Now, rearranging the formula to solve for ΔT:
ΔT = Q / (m * c)
ΔT = 3135 J / (1.45 kg * 450 J/kg·°C)
ΔT ≈ 4.10 °C
So, the change in temperature of the skillet is approximately 4.10 °C.