Question

Consider the substances in Table 6.1. Which substance requires the largest amount of energy to raise the temperature of \(25.0 \mathrm{~g}\) of the substance from \(15.0^{\circ} \mathrm{C}\) to \(37.0^{\circ} \mathrm{C} ?\) Calculate the energy. Which substance in Table \(6.1\) has the largest temperature change when \(550 . \mathrm{g}\) of the substance absorbs \(10.7 \mathrm{~kJ}\) of energy? Calculate the temperature change.

Short answer

The substance that requires the largest amount of energy to raise the temperature of 25.0 g from 15.0°C to 37.0°C can be found using the specific heat capacity formula \(q = mc\Delta T\). Upon comparing the calculated heat energy (q) required for each substance in Table 6.1 to achieve the given temperature change, we can determine the substance that requires the largest amount of energy. To find the substance with the largest temperature change when 550 g of it absorbs 10.7 kJ (10,700 J) of energy, we can utilize the formula again, rearranging to solve for the temperature change: \(\Delta T = \frac{q}{mc}\). Comparing the calculated temperature changes for each substance, we can identify the one with the largest change in temperature.

Step-by-step solution

Finding the specific heat capacities

Look up the specific heat capacities (c) for each substance in Table 6.1.

Calculate heat energy needed

Use the specific heat capacity formula \(q = mc\Delta T\) for each substance. - mass (m) = 25.0 g - change in temperature (\(\Delta T = T_{final} - T_{initial}\)) = 37.0°C - 15.0°C = 22.0°C For each substance, plug in the mass, specific heat capacity, and change in temperature to calculate the heat energy (q) required.

Find the substance requiring the largest heat energy

Compare the calculated heat energy (q) for each substance and find the one that requires the largest amount of energy.

Calculate the temperature change for the given absorbed energy

We are given that 550 g of the substance absorbs 10.7 kJ (10,700 J) of energy. Use the formula again, but now solve for the temperature change (\(\Delta T\)) instead. \( \Delta T = \frac{q}{mc} \) For each substance, plug in the mass, specific heat capacity, and given absorbed energy to calculate the temperature change.

Find the substance with the largest temperature change

Compare the calculated temperature changes for each substance and find the one with the largest temperature change.

Key concepts

Heat Energy Calculation

Understanding how to calculate heat energy is crucial for many scientific and engineering applications. Heat energy, often measured in joules (J), is the energy transferred from one body or system due to a temperature difference.

The formula to calculate the heat energy required to change the temperature of a substance is given by: \[ q = mc\Delta T \]Here,

• \( q \) is the heat energy in joules,
• \( m \) is the mass of the substance in grams,
• \( c \) is the specific heat capacity, usually in joules per gram per degree Celsius (\(\frac{J}{g^\circ C}\)), and
• \( \Delta T \) is the change in temperature in Celsius (\( \Delta T = T_{final} - T_{initial} \)).

To solve for \( q \), you multiply the mass of the substance by its specific heat capacity and the change in temperature. The specific heat capacity is a property that indicates how much heat energy a substance requires to raise its temperature by one degree Celsius. It varies from substance to substance, reflecting how different materials respond to heat.

In our practical problem, finding the heat energy necessary to raise the temperature of different substances is critical for comparing their thermal properties. By plugging in the values from the given substances, you can calculate the heat energy each requires for a specified temperature change.

Temperature Change

Temperature change is a fundamental concept in thermodynamics, indicating the degree of increase or decrease in the heat energy within a substance. As seen in the exercise, temperature change (\( \Delta T \)) is the difference between the final temperature (\( T_{final} \)) and the initial temperature (\( T_{initial} \)).

In practical terms, understanding temperature change is important for a variety of applications, such as designing thermal systems or understanding weather patterns.

To calculate the temperature change that results from absorbing or releasing heat, the formula is rearranged to: \[ \Delta T = \frac{q}{mc} \]By dividing the heat energy (\( q \)) by the product of the mass (\( m \)) and the specific heat capacity (\( c \)), we find out how much the temperature of the substance will change as a result of the energy transfer. It's important to note that this equation assumes no phase change (like melting or boiling) occurs within the temperature range given. If a phase change were to occur, additional heat (latent heat) would be involved without a change in temperature.

When solving problems like the one in our exercise, calculating temperature change allows students to compare how different materials respond to the absorption of a set amount of heat energy.

Endothermic Processes

Endothermic processes involve the absorption of heat energy from the surroundings, which results in a temperature rise within the system or material. In chemistry and physics, these processes are key to understanding how energy changes during chemical reactions or when states of matter change.

Typical examples of endothermic processes include melting ice, evaporating liquid water, and cooking an egg. During these processes, energy is absorbed to break bonds or change the structure of the material. For a given mass, the specific heat capacity helps predict how much heat will need to be absorbed to achieve a desired temperature change, as seen in the exercise we're analyzing.

The concept also applies to the problem at hand, which involves calculating the energy necessary to increase the temperature of various substances. Each substance requires a distinct amount of heat energy for its temperature to rise, reflective of its endothermic capabilities. The larger the specific heat capacity, the more heat a substance can store, making it capable of undergoing significant endothermic processes without a large temperature increase.

Grasping this concept helps students appreciate how different materials interact with heat, which is essential for applications ranging from culinary arts to material sciences.