Problem 58 - Chemistry Matter and Change

Question

What quantity has the units \(\mathrm{J} /\left(\mathrm{g} \cdot^{\circ} \mathrm{C}\right) ?\)

Step-by-Step Solution

Answer

The quantity is specific heat capacity.

Step 1: Identify the Units

The units given in the question are \( \mathrm{J} /(\mathrm{g} \cdot^{\circ} \mathrm{C}) \). These units are a way to describe how much energy is needed to change the temperature of a certain mass by a certain amount.

Step 2: Relate Units to Physical Quantity

The units \( \mathrm{J} /(\mathrm{g} \cdot^{\circ} \mathrm{C}) \) are related to a quantity known as 'specific heat capacity'. Specific heat capacity measures how much heat energy is required to raise the temperature of one gram of a substance by one degree Celsius.

Step 3: Conclusion

Based on the units given, \( \mathrm{J} /(\mathrm{g} \cdot^{\circ} \mathrm{C}) \) represents the specific heat capacity of a substance.

Key Concepts

Units of Measurement

Units of measurement are crucial in science to ensure accurate and consistent communication. When dealing with specific heat capacity, the units we often see are joules per gram-degree Celsius \( \mathrm{J} / (\mathrm{g} \cdot^{\circ} \mathrm{C}) \).These units might seem a bit complex at first, but they break down very logically.

• Joules (J): The basic unit of energy in the International System of Units (SI).
• Grams (g): A commonly used unit of mass.
• Degrees Celsius (ºC): A temperature scale that measures thermal energy.

The combination of these units allows us to describe the energy needed to affect a change in temperature. In this case, we are talking specifically about raising the temperature of one gram of a material by one degree Celsius.With these units, scientists can compare how different materials use energy. It helps us understand processes like heating and cooling much better.

Thermal Energy

Thermal energy refers to the energy that comes from the temperature of matter. The more thermal energy a substance has, the hotter it is. In the context of specific heat capacity, thermal energy plays a crucial role. This is the energy that you provide to change a substance’s temperature. When you heat an object, you increase its thermal energy by adding joules. The object’s specific heat capacity will dictate how many joules are needed. While each substance has its unique capacity to hold thermal energy, those with a high specific heat capacity require more energy to achieve the same temperature change than those with a low specific heat capacity. The concept of thermal energy and specific heat helps explain everyday phenomena. Consider why water takes longer to heat up than oil: it’s due to water’s higher specific heat capacity.

Temperature Change

Temperature change is the resulting difference when a substance's internal energy changes due to heating or cooling. Understanding how temperature changes occur helps us better grasp specific heat capacity.The formula to calculate energy from temperature change is: \( q = m \cdot c \cdot \Delta T \) where:

• \( q \) = thermal energy in joules
• \( m \) = mass in grams
• \( c \) = specific heat capacity
• \( \Delta T \) = change in temperature (final temperature - initial temperature)

This formula allows us to calculate how much energy is required to increase or decrease the temperature of a given mass by a certain number of degrees.By understanding this relationship, you gain insight into how substances react to heat and more effectively manage processes involving temperature change. It's a key concept in areas like cooking, engineering, and environmental science.