A 35g sample of Fe is dropped into 80g of water at 20 degrees Celsius. What is the final (equilibrium) temperature of the iron/water?
This isn't really a chemistry problem. There will be no chemical reaction. It is a heat capacity (physics) problem.
Use the specfic heats of iron and water, and set the heat loss of the iron equal to the heat gain of the water, when reaching the final temperature Tf.
35*CFe*(80 - Tf) = 80*Cw*(Tf-20)
CFe is the specific heat of Fe and Cw is the specific hdeat of water. Look up CFe and solve for Tf.
To find the final equilibrium temperature of the iron/water system, you can use the principle of heat transfer and the specific heat capacities of the iron and water.
Specific heat capacity (C) is the amount of heat energy required to raise the temperature of a substance by 1 degree Celsius. In this case, you need to use the specific heat capacities of iron (CFe) and water (Cw).
Here's how you can calculate the final temperature (Tf):
1. Look up the specific heat capacity of iron (CFe) and water (Cw). These values can typically be found in reference tables. Let's assume the specific heat capacity of iron is 0.45 J/g°C, and the specific heat capacity of water is 4.18 J/g°C.
2. Use the principle of heat transfer, which states that the heat lost by the iron will be equal to the heat gained by the water at equilibrium. The heat gained or lost can be calculated using the formula:
Heat gained/lost = mass × specific heat capacity × temperature change
3. Set up an equation using the heat gained and heat lost values:
35g × CFe × (80°C - Tf) = 80g × Cw × (Tf - 20°C)
Here, 35g is the mass of the iron, 80g is the mass of the water, 80°C is the initial temperature of the water, and 20°C is the initial temperature of the iron.
4. Solve the equation for Tf. Rearrange the equation to isolate Tf on one side:
35g × CFe × (80°C - Tf) = 80g × Cw × (Tf - 20°C)
Simplify: 35g × CFe × 80°C - 35g × CFe × Tf = 80g × Cw × Tf - 80g × Cw × 20°C
Rearrange: 35g × CFe × 80°C - 80g × Cw × Tf = 35g × CFe × Tf - 80g × Cw × 20°C
Combine like terms: (35g × CFe - 35g × Cw) × Tf = 80g × Cw × 20°C - 35g × CFe × 80°C
Divide both sides by (35g × CFe - 35g × Cw) to solve for Tf:
Tf = (80g × Cw × 20°C - 35g × CFe × 80°C) / (35g × CFe - 35g × Cw)
5. Plug in the specific heat capacities and solve for Tf using the equation:
Tf = (80g × 4.18 J/g°C × 20°C - 35g × 0.45 J/g°C × 80°C) / (35g × 0.45 J/g°C - 35g × 4.18 J/g°C)
Calculate the numerator and denominator separately, and then divide to find the final temperature Tf.