Problem 67 - Chemistry Matter and Change

Question

Metallurgy \(\mathrm{A} 25.0\) -g bolt made of an alloy absorbed 250 \(\mathrm{J}\) of heat as its temperature changed from \(25.0^{\circ} \mathrm{C}\) to \(78.0^{\circ} \mathrm{C} .\) What is the specific heat of the alloy?

Step-by-Step Solution

Answer

The specific heat of the alloy is approximately \( 188.68 \text{ J/kg} \cdot \text{°C} \).

Step 1: Identify Known Values

We are given that the bolt absorbed a total heat energy of 250 J, has a mass of 25.0 g, and the temperature change is from \( 25.0^{\circ} \mathrm{C} \) to \( 78.0^{\circ} \mathrm{C} \).

Step 2: Calculate Temperature Change

The temperature change \( \Delta T \) is calculated as the difference between the final temperature and the initial temperature: \[ \Delta T = 78.0^{\circ} \mathrm{C} - 25.0^{\circ} \mathrm{C} = 53.0^{\circ} \mathrm{C} \]

Step 3: Use Specific Heat Capacity Formula

The specific heat capacity \( c \) is calculated using the formula \[ q = mc\Delta T \] where \( q = 250 \text{ J} \) is the heat energy absorbed, \( m = 25.0 \text{ g} = 0.025 \text{ kg} \) is the mass, and \( \Delta T = 53.0^{\circ} \mathrm{C} \).

Step 4: Solve for Specific Heat Capacity

Rearrange the formula to solve for \( c \):\[ c = \frac{q}{m\Delta T} \] Substitute the known values:\[ c = \frac{250 \text{ J}}{0.025 \text{ kg} \times 53.0^{\circ} \mathrm{C}} \approx 188.68 \text{ J/kg} \cdot \text{°C} \]

Step 5: Conclude with Specific Heat

The specific heat capacity of the alloy is approximately \( 188.68 \text{ J/kg} \cdot \text{°C} \).

Key Concepts

Understanding Metallurgy

Metallurgy is the scientific field that focuses on the physical and chemical behaviors of metallic elements and their mixtures known as alloys.
Metallurgists study metals to understand how they can be manipulated and used for various applications.
Like witches creating potions, they mix metals to form new compounds with unique properties.

• They assess things like malleability, ductility, and conductivity.
• This knowledge is crucial in industries like automotive, aerospace, and even jewelry making.

Grasping the basics of metallurgy helps us figure out why a particular metal or alloy would be chosen for a specific task, such as constructing a durable bolt.

Comprehending Heat Energy

Heat energy, often referred to as thermal energy, is an important concept in understanding how materials like metals and alloys behave under different temperatures.
It is the energy that is transferred from one body to another as a result of a temperature difference.

• When heat energy is absorbed, it causes the atoms and molecules within a substance to move faster, leading to an increase in temperature.
• The amount of heat energy required to change the temperature depends on the material's specific heat capacity.

Heat energy can change the physical state of a material, and a clear grasp of this concept helps in applications like forging metal parts or making alloys.

Exploring Temperature Change

Temperature change refers to the difference in temperature that a substance undergoes when heat is either absorbed or lost.
In the context of metallurgy and materials science, understanding temperature change is critical to predicting how metals and alloys will react in different settings.
The temperature change can affect:

• The structural integrity of a metal.
• The potential for it to expand or contract.
• The capability of a metal to conduct heat or electricity.

Engineers and scientists calculate temperature change using the simple formula \[\Delta T = T_{final} - T_{initial}\]which helps in determining the thermal properties and appropriate applications for metals.

Significance of Alloys

An alloy is a mixture of metals, or a metal combined with one or more other elements.
This process usually enhances the properties of individual metals and results in materials that are more suitable for practical applications.

• Alloys can be tougher, more resistant to corrosion, and have improved thermal and electrical properties compared to their component metals.
• Examples include steel, brass, and bronze.

Understanding alloys allows manufacturers to create custom materials that have the desired properties needed for specific technologies.
In our exercise, the bolt was made of an alloy, which could likely have been designed for strength and durability, making it perfect for situations where reliable components are a must.