Math Problem Statement
Solution
To solve this problem, we need to use the principle of conservation of energy, specifically heat transfer between the metal and the water.
Step-by-Step Solution:
-
Identify the Known Values:
- Mass of the metal (): 80.77 g
- Initial temperature of the metal (): 100.0°C
- Mass of water (): 100.0 g
- Specific heat of water (): 4.18 J/g°C
- Initial temperature of water (): 25.0°C
- Final temperature of both water and metal (): 30.0°C
-
Calculate the Heat Gained by Water: The heat gained by the water () can be calculated using the formula: Substituting the values:
-
Apply the Conservation of Energy: Since the heat lost by the metal equals the heat gained by the water, we have:
-
Calculate the Specific Heat of the Metal: Using the formula for heat transfer, , we rearrange to find the specific heat () of the metal: Substituting the values:
-
Identify the Metal: From the given choices, the specific heat value closest to 0.4605 J/g°C corresponds to iron.
Answer:
The metallic solid is iron.
Would you like further explanation on any step?
Here are some follow-up questions to deepen understanding:
- What is the principle of conservation of energy and how is it applied in this scenario?
- How would the answer change if the mass of water was different?
- Why is it important to reach thermal equilibrium in this type of problem?
- How does specific heat relate to a material's ability to retain heat?
- Can you think of real-life applications of specific heat capacity in material selection?
Tip: Always check units for consistency when working with heat transfer problems to avoid calculation errors.
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Thermodynamics
Heat Transfer
Specific Heat Capacity
Formulas
q = mcΔT
q_water = m_water * c_water * (T_final - T_initial, water)
q_metal = m_metal * c_metal * (T_initial, metal - T_final)
Theorems
Conservation of Energy
Suitable Grade Level
Grades 9-12
Related Recommendation
Calculating Specific Heat of Metal Using Heat Transfer Formula
Calculate the Specific Heat of a Metal Using Heat Transfer Principles
Calculate the Specific Heat Capacity of a Metal Using Heat Transfer
Finding the Mass of Copper Using Heat Transfer and Energy Conservation
How to Calculate Specific Heat of a Metal in a Calorimetry Problem