Calorimetry Problem: Calculating the Mass of a Steel Rod

What is the specific heat of water and steel? How can we calculate the mass of the steel rod based on the given data? The specific heat of water is 4.184 J/(g⋅∘C) and the specific heat of steel is 0.452 J/(g⋅∘C). To calculate the mass of the steel rod, we can use the principles of calorimetry and the Law of Conservation of Energy.

Calorimetry and Conservation of Energy

Equation:

According to the Law of Conservation of Energy, the heat flow into an object must equal the heat flow out of the object, resulting in a total change of zero. The formula for heat transfer is q = mCΔT, where q is the heat transferred, m is the mass of the sample, C is the specific heat capacity, and ΔT is the change in temperature.

Calculations:

In this problem, we have the initial temperature of water, the final temperature of the system, and the specific heat capacities of water and steel. By setting up the equation with the heat flows from the steel rod and into the water, we can calculate the mass of the steel rod.

Calculating the Mass of the Steel Rod

Given data:

  • Initial temperature of water: 24.00 °C
  • Final temperature of the system: 21.20 °C
  • Specific heat of water: 4.184 J/(g⋅∘C)
  • Specific heat of steel: 0.452 J/(g⋅∘C)
  • Volume of water: 150.0 mL

Calculation Steps:
  1. Calculate the heat absorbed by the steel rod and the water based on the given temperatures and specific heat capacities.
  2. Use the Law of Conservation of Energy to set up an equation equating the two heat flows.
  3. Determine the mass of the steel rod using the calculated values and the equation derived from the conservation of energy.

By following these steps and performing the necessary calculations, we can find that the mass of the steel rod in this scenario is 207 grams.

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