Question

A piece of iron with mass of 25.0 g is at 398 K. It is placed into a styrofoam coffee cup containing 25.0 mL of water that is at 298 K. Assuming that no heat is lost to the cup or the surroundings, what will the final temperature of the water be? The density of water is 1.00 g/mL, the specific heat of iron is 0 . 449 J / g · ° C and the specific heat of water is 4 . 18 J / g · ° C .

Answer 1

To find the final temperature of the water, we can use the principle of conservation of energy. The heat gained by the water is equal to the heat lost by the iron. Using the given values and equations, we can calculate the final temperature of the water to be approximately 338 K (65°C).

Step-by-step explanation:

To find the final temperature of the water, we can use the principle of conservation of energy. The heat gained by the water is equal to the heat lost by the iron. We can calculate the heat gained by the water using the equation:

q = m * c * ΔT

where q is the heat gained, m is the mass of the water, c is the specific heat of water, and ΔT is the change in temperature.

Using the given values, we have:
q = 25.0 g * 4.18 J/g °C * (T - 298 K)

where T is the final temperature of the water. We can calculate the heat lost by the iron using the equation:

q = m * c * ΔT

where q is the heat lost, m is the mass of the iron, c is the specific heat of iron, and ΔT is the change in temperature.

Using the given values, we have:
q = 25.0 g * 0.449 J/g °C * (398 K - T)

Since no heat is lost to the cup or the surroundings, the heat gained by the water is equal to the heat lost by the iron:

25.0 g * 4.18 J/g °C * (T - 298 K) = 25.0 g * 0.449 J/g °C * (398 K - T)

Simplifying the equation, we get:
4.18 (T - 298) = 0.449 (398 - T)

After solving for T, the final temperature of the water is approximately 338 K (65°C).