Chapter 3: Problem 75
Calculate the amount of heat required to raise the temperature of a 65-g sample of water from \(32{ }^{\circ} \mathrm{C}\) to \(65{ }^{\circ} \mathrm{C}\).
Short Answer
Expert verified
The amount of heat required is 8974.5 J.
Step by step solution
01
Understanding the problem
We are given the mass of water (65 g), the initial temperature (32 degrees Celsius), and the final temperature (65 degrees Celsius). We need to find the amount of heat required to raise the temperature of the water from the initial temperature to the final temperature. This can be calculated using the specific heat capacity formula: Q = mcΔT, where Q is the heat energy, m is the mass, c is the specific heat capacity (for water, it is approximately 4.18 J/g°C), and ΔT is the change in temperature.
02
Calculate the change in temperature
Firstly, we must calculate the change in temperature (ΔT). ΔT = final temperature - initial temperature. For water, ΔT = 65°C - 32°C = 33°C.
03
Apply the specific heat capacity formula
Using the specific heat capacity formula Q = mcΔT: Q = (65 g)(4.18 J/g°C)(33°C). Multiply the mass, specific heat capacity, and change in temperature to find the heat required.
04
Perform the calculation
Q = (65 g)(4.18 J/g°C)(33°C) = 8974.5 J. The heat required is therefore 8974.5 Joules.
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
Specific Heat Capacity
Specific heat capacity is a property of matter that describes how much heat energy is required to raise the temperature of one gram of a substance by one degree Celsius (or one Kelvin). In simpler terms, it tells us how 'resistant' a substance is to changing its temperature when we add or remove heat. Water, for instance, has a high specific heat capacity of approximately 4.18 Joules per gram per degree Celsius (\(4.18 \frac{J}{g\textdegree C}\)), which means it requires a lot of energy to change its temperature. This property accounts for water's ability to moderate temperatures in its surroundings, such as in oceans and human bodies.
Understanding specific heat capacity is essential when dealing with heat transfer in various applications, including cooking, heating and cooling systems, and even weather patterns. The concept is present in many scientific calculations and practical applications, from designing thermal systems to predicting how a cup of coffee cools down.
To compute the specific heat capacity when it's unknown, we can rearrange the formula used in the exercise (\(Q = mc\textDelta T\)) to solve for 'c', where 'm' is mass, 'Q' is heat energy, and '\textDelta T' is the temperature change. This formula thus becomes \[c = \frac{Q}{m\textDelta T}\]. It plays a pivotal role in understanding how different materials react to heat and is crucial for tasks requiring precise temperature regulation.
Understanding specific heat capacity is essential when dealing with heat transfer in various applications, including cooking, heating and cooling systems, and even weather patterns. The concept is present in many scientific calculations and practical applications, from designing thermal systems to predicting how a cup of coffee cools down.
To compute the specific heat capacity when it's unknown, we can rearrange the formula used in the exercise (\(Q = mc\textDelta T\)) to solve for 'c', where 'm' is mass, 'Q' is heat energy, and '\textDelta T' is the temperature change. This formula thus becomes \[c = \frac{Q}{m\textDelta T}\]. It plays a pivotal role in understanding how different materials react to heat and is crucial for tasks requiring precise temperature regulation.
Temperature Change
Temperature change, denoted as \(\textDelta T\), is a measure of the difference between the final and initial temperatures, essentially reflecting how much the temperature of a substance has increased or decreased. It is a key variable in thermodynamics and plays a crucial role in heat energy calculations, such as the one in our exercise where water's temperature is raised from 32 to 65 degrees Celsius.
When calculating the amount of heat (\(Q\)) to change the temperature of a substance, \(\textDelta T\) is central because it represents the extent of heating or cooling needed. In everyday life, temperature change is something we always consider, like when we adjust the thermostat to heat or cool a room or when we wait for a cup of tea to cool to a drinkable temperature.
In the context of the exercise, the temperature change from 32 to 65 degrees Celsius (a \(\textDelta T\) of 33 degrees Celsius) tells us the extent of energy required to achieve the desired increase in temperature. The greater the \(\textDelta T\), the more heat energy needed, if the substance's specific heat capacity remains constant. This principle has practical implications, for example, in designing thermal systems where the goal is to achieve a specific temperature range efficiently.
When calculating the amount of heat (\(Q\)) to change the temperature of a substance, \(\textDelta T\) is central because it represents the extent of heating or cooling needed. In everyday life, temperature change is something we always consider, like when we adjust the thermostat to heat or cool a room or when we wait for a cup of tea to cool to a drinkable temperature.
In the context of the exercise, the temperature change from 32 to 65 degrees Celsius (a \(\textDelta T\) of 33 degrees Celsius) tells us the extent of energy required to achieve the desired increase in temperature. The greater the \(\textDelta T\), the more heat energy needed, if the substance's specific heat capacity remains constant. This principle has practical implications, for example, in designing thermal systems where the goal is to achieve a specific temperature range efficiently.
Heat Transfer in Chemistry
Heat transfer in chemistry is a foundational concept that refers to the movement of thermal energy from one body or system to another. This transfer occurs in three primary ways: conduction, convection, and radiation. In the context of the exercise provided, we are mostly concerned with the conduction of heat in a substance—how heat flows through materials like the water being heated from 32 to 65 degrees Celsius.
In a chemical laboratory, understanding heat transfer is essential for controlling reactions which often require precise temperatures to ensure proper activation and completion. It also helps in designing experiments—for instance, using a water bath to evenly distribute heat to reaction vessels.
Furthermore, in industrial processes, heat transfer principles guide the design of equipment, such as reactors and heat exchangers, to optimize energy consumption and safety. Heat transfer is not only a key theme in thermodynamics but also integral to a variety of real-world applications, including culinary arts, engine cooling systems, climate control, and the creation of comfortable living and working environments.
Through the practical use of heat transfer, chemists and engineers develop efficient processes to manage the flow of heat, either to enhance it or curtail it, depending on the desired outcome. The exercise's focus on calculating the heat required for a given temperature change illustrates how important it is to understand this concept to translate theoretical knowledge into practical solutions.
In a chemical laboratory, understanding heat transfer is essential for controlling reactions which often require precise temperatures to ensure proper activation and completion. It also helps in designing experiments—for instance, using a water bath to evenly distribute heat to reaction vessels.
Furthermore, in industrial processes, heat transfer principles guide the design of equipment, such as reactors and heat exchangers, to optimize energy consumption and safety. Heat transfer is not only a key theme in thermodynamics but also integral to a variety of real-world applications, including culinary arts, engine cooling systems, climate control, and the creation of comfortable living and working environments.
Through the practical use of heat transfer, chemists and engineers develop efficient processes to manage the flow of heat, either to enhance it or curtail it, depending on the desired outcome. The exercise's focus on calculating the heat required for a given temperature change illustrates how important it is to understand this concept to translate theoretical knowledge into practical solutions.
