A 455-g chunk of iron is removed from an oven and plunged into 385g water in an insulated container. The temperature of the water increases from 27 degrees celsius to 89 degrees celsius.
If the specific heat of iron is 0.449 J g^-1 degrees Celsius^-1, what must have been the original temperature of the iron?
heat lost by the iron + heat gained by water = 0.
[massFe x specific heatFe x (Tfinal-Tinitial)] + [mass water x specific heat water x (Tfinal-Tinitial)] = 0
Only one unknown, Tinitial Fe.
How do I figure out the final Fe?
How do you find out the final Fe
To calculate the original temperature of the iron, we can use the principle of conservation of energy. The energy gained by the water is equal to the energy lost by the iron.
The energy gained by the water can be calculated using the formula:
Energy gained = mass of water (g) * specific heat of water (J g^-1 degrees Celsius^-1) * change in temperature of water (degrees Celsius)
Given:
- Mass of water (m1) = 385 g
- Specific heat of water (c1) = 4.184 J g^-1 degrees Celsius^-1
- Change in temperature of water (Δt1) = 89 degrees Celsius - 27 degrees Celsius = 62 degrees Celsius
So, the energy gained by the water is:
Energy gained = 385 g * 4.184 J g^-1 degrees Celsius^-1 * 62 degrees Celsius
Now, using the principle of conservation of energy, we know that the energy gained by the water is equal to the energy lost by the iron:
Energy lost by iron = mass of iron (g) * specific heat of iron (J g^-1 degrees Celsius^-1) * change in temperature of iron (degrees Celsius)
Given:
- Mass of iron (m2) = 455 g
- Specific heat of iron (c2) = 0.449 J g^-1 degrees Celsius^-1
- Change in temperature of iron (Δt2) = original temperature of iron - final temperature of iron (unknown)
Using the conservation of energy equation, we can write:
Energy gained = Energy lost
385 g * 4.184 J g^-1 degrees Celsius^-1 * 62 degrees Celsius = 455 g * 0.449 J g^-1 degrees Celsius^-1 * (original temperature of iron - 89 degrees Celsius)
Now, we can solve for the original temperature of the iron by rearranging the equation and solving for the unknown:
(original temperature of iron - 89 degrees Celsius) = (385 g * 4.184 J g^-1 degrees Celsius^-1 * 62 degrees Celsius) / (455 g * 0.449 J g^-1 degrees Celsius^-1)
(original temperature of iron - 89 degrees Celsius) = 28488.04 / 204.895
(original temperature of iron - 89 degrees Celsius) = 138.958
Finally, adding 89 degrees Celsius to both sides of the equation, we get:
original temperature of iron = 138.958 + 89 degrees Celsius
Therefore, the original temperature of the iron is approximately 227.958 degrees Celsius.