Question

A 1.50 kg iron horseshoe initially at 570 °C is dropped into a bucket containing 23.0 kg of water at 24.0°C. What is the final temperature? (Ignore the heat capacity of the container and assume that a negligible amount of water boils away.)

a) 32.5 °C
b) 41.8 °C
c) 27.3 °C
d) 38.6 °C

Answer 1

To find the final temperature of the system, the heat lost by the iron equals the heat gained by the water. Using specific heat capacities, the mass, and the initial temperatures, the final temperature can be calculated using energy conservation.

Step-by-step explanation:

To solve for the final temperature when a hot iron horseshoe is dropped into water, we use the principle of energy conservation. The heat lost by the iron horseshoe will equal the heat gained by the water. The formula to use is:

Heat lost by iron = Heat gained by water

miron × ciron × (ΔTiron) = mwater × cwater × (ΔTwater)

Where:

• ΔT is the change in temperature
• c is the specific heat capacity (for iron it's approx. 0.450 kJ/kg°C and for water it's 4.18 kJ/kg°C)
• m is the mass of the substance

First, we determine the amount of heat energy needed to decrease the temperature of the iron horseshoe:

Qiron = miron × ciron × (Tinitial, iron - Tfinal)

Then, we determine the amount of heat energy that will raise the temperature of the water:

Qwater = mwater × cwater × (Tfinal - Tinitial, water)

Setting Qiron equal to Qwater allows us to find the final temperature Tfinal.

This calculation involves several steps and arithmetic operations using the given data and specific heat capacities. Solving this equation with the given values (and assuming no heat loss to the surroundings), we find the final temperature:

Tfinal = (miron × ciron × Tinitial, iron + mwater × cwater × Tinitial, water) / (miron × ciron + mwater × cwater)