Question

A 75.0 g piece of iron metal at 98°C is placed in 200.0 g of water originally at 22.5°C. Calculate the final temperature of the iron and water, after they reach thermal equilibrium. The specific heat, Cp, of iron is 0.45 J/(g•°C), and that for water is 4.18 J/(g•°C).

A. 36.2°C
B. 39.8°C
C. 42.1°C
D. 45.5°C

Answer 1

To find the final temperature of the iron and water after reaching thermal equilibrium, use the equation for heat transfer and set the heat transferred to the iron equal to the heat transferred to the water. After solving the equation, the final temperature is found to be 42.1°C.

Step-by-step explanation:

To solve this problem, we can use the equation for heat transfer: q = mcΔT, where q is the heat transferred, m is the mass of the object, c is the specific heat capacity, and ΔT is the change in temperature.

First, calculate the heat transferred to the iron: q iron = 75.0 g × 0.45 J/(g·°C) × (Ft - 98°C), where Ft is the final temperature of the iron.

Next, calculate the heat transferred to the water: q water = 200.0 g × 4.18 J/(g·°C) × (Ft - 22.5°C), where Ft is the final temperature of the water is found to be 42.1°C.

Since the total heat transferred to the iron and water is equal at thermal equilibrium, we can set the two equations equal to each other and solve for Ft.