Problem 49 - Chemistry: An Atoms-Focused Approach

Question

How much heat must be absorbed by \(100.0 \mathrm{g}\) of water to raise its temperature from \(30.0^{\circ} \mathrm{C}\) to \(100.0^{\circ} \mathrm{C} ?\)

Step-by-Step Solution

Answer

Question: Calculate the amount of heat that must be absorbed by 100 grams of water to raise its temperature from 30°C to 100°C. Answer: The amount of heat that must be absorbed by the water is 29260 J.

Step 1: Note down the known values

We know the following values: - mass of water (\(m\)) = \(100.0 \mathrm{g}\) - specific heat capacity of water (\(c\)) = \(4.18 \mathrm{J / (g°C)}\) - initial temperature (\(T_i\)) = \(30.0^{\circ} \mathrm{C}\) - final temperature (\(T_f\)) = \(100.0^{\circ} \mathrm{C}\)

Step 2: Calculate the change in temperature

To calculate the change in temperature (\(ΔT\)), we subtract the initial temperature from the final temperature: \(ΔT = T_f - T_i\) \(ΔT = 100.0^{\circ} \mathrm{C} - 30.0^{\circ} \mathrm{C}\) \(ΔT = 70.0^{\circ} \mathrm{C}\)

Step 3: Apply the specific heat capacity formula

Now we will apply the specific heat capacity formula: \(Q = mcΔT\) where: - \(Q\) is the heat absorbed by water - \(m\) is the mass of water (\(100.0 \mathrm{g}\)) - \(c\) is the specific heat capacity of water (\(4.18 \mathrm{J / (g°C)}\)) - \(ΔT\) is the change in temperature (\(70.0^{\circ} \mathrm{C}\))

Step 4: Calculate the heat absorbed

Now, we will plug in the values in the formula: \(Q = (100.0 \mathrm{g})(4.18 \mathrm{J / (g°C)})(70.0^{\circ} \mathrm{C})\) \(Q = 29260 \mathrm{J}\) The amount of heat that must be absorbed by the water is \(29260 \mathrm{J}\).

Key Concepts

Heat Absorption

To understand how heat is absorbed by a substance, we first need to appreciate the role of specific heat capacity. Specific heat capacity defines how much energy is needed to raise the temperature of one gram of a material by one degree Celsius. In our exercise, the specific heat capacity of water is given as 4.18 J/(g°C). This means water can absorb a fair amount of energy without its temperature changing drastically.

When we talk about heat absorption, we refer to the energy transfer that increases the temperature of a substance rather than changing its state or chemical composition. In our example, water absorbs heat to move from 30°C to 100°C. The energy absorbed is calculated using the formula:

• \(Q = mcΔT\)

Where \(Q\) is the total heat absorbed, \(m\) stands for mass in grams, \(c\) is specific heat capacity, and \(ΔT\) represents the temperature change in Celsius. As you can see, \(Q\) is directly proportional to these variables, which means the greater the mass or temperature change, the more heat is absorbed.

Temperature Change

Temperature change is a straightforward concept but a crucial one in thermodynamics and heat transfer. It is simply the difference between the final and initial temperatures of a substance. In mathematical terms, it's expressed as:

• \(ΔT = T_f - T_i\)

In the given problem, the water experiences a temperature change from 30°C to 100°C, which results in a \(ΔT\) of 70°C.

The significance of temperature change lies in its direct impact on the amount of heat absorbed by a substance. Larger temperature changes mean more energy is needed, and this is where our calculation from the exercise becomes handy. By knowing the temperature change, and with the specific heat capacity of the material, you can determine how much heat is absorbed using the calculation we've discussed earlier.

Thermodynamics

Thermodynamics is the field of physics that deals with the relationships between heat, work, and energy. In essence, it's about how energy is transferred within a system and the effects it has.

In our everyday experience, when we perform a calculation like our initial example, we're applying the first law of thermodynamics—or the principle of energy conservation. This states that energy cannot be created or destroyed; it can only change forms. When heat energy is absorbed by the water, it doesn't disappear. Instead, it increases the kinetic energy of the water molecules, resulting in a temperature rise.

This understanding is essential because it helps us predict and control the energy use in various applications, from heating systems to even understanding meteorological phenomena. It shows that detailed knowledge of heat capacity and temperature changes enable us to harness thermal energy more effectively. Thus, studying thermodynamics is not just about solving textbook problems but about understanding how energy moves and transforms around us.