Question

In the "Chemistry in Focus" segment Firewalking: Magic or Science?, it is claimed that one reason people can walk on hot coals is that human tissue is mainly composed of water. Because of this, a large amount of heat must be transferred from the coals to change the temperature of the feet significantly. How much heat must be transferred to \(100.0 \mathrm{~g}\) of water to change its temperature by 35 "C ?

Short answer

To change the temperature of 100.0 g of water by 35°C, 14630 J of heat must be transferred.

Step-by-step solution

Identify the given variables

We are given the following values: - m (mass of water) = 100.0 g - c (specific heat capacity of water) = 4.18 J/g°C - ΔT (change in temperature) = 35°C

Substitute the given values into the formula

Now we can substitute the given values into the heat transfer formula: \(q = (100.0 \mathrm{~g})(4.18 \mathrm{~J/g~^\circ C})(35^\circ \mathrm{C})\)

Calculate the heat transfer

Perform the multiplication to find the heat transfer: \(q = 100.0 \times 4.18 \times 35\) \(q = 14630 \mathrm{~J}\)

Write the final answer

The amount of heat that must be transferred to the 100.0 g of water to change its temperature by 35°C is: \(q = 14630 \mathrm{~J}\)

Key concepts

Specific Heat Capacity

In the realm of physics and chemistry, the term specific heat capacity (often simply referred to as specific heat) is crucial for understanding how different substances respond to the addition or loss of heat. Specific heat capacity is defined as the amount of heat energy required to raise the temperature of one gram of a substance by one degree Celsius (or one Kelvin). The unique value for each substance determines how much energy is needed to change its temperature.

For instance, water has a high specific heat capacity, meaning it can absorb a lot of heat before it starts to get hot. This property explains why water is effective in cooling systems and also why it poses a challenge when trying to heat it up efficiently. The specific heat of water is approximately 4.18 Joules per gram per degree Celsius (\(4.18 \frac{J}{g\degree C}\)), which is higher than many other common substances, showcasing its impressive capacity to store heat.

This characteristic comes into play in activities such as firewalking, as mentioned in the 'Chemistry in Focus' segment. The human body, which mainly consists of water, will not rise significantly in temperature when brief contact is made with hot coals, due to water's high specific heat. The heat from the coal isn't enough to instantly change the temperature of the water-rich tissues, thereby protecting the feet from immediate burns.

Temperature Change in Chemistry

Temperature change in chemistry refers to the variation of heat content within substances which results from various chemical processes or physical changes. It's the observable difference in a substance's temperature before and after an event, such as a reaction or exposure to a heat source. Understanding this concept helps in predicting the outcomes of chemical reactions and designing systems for thermal management.

In many laboratory and industrial processes, controlling the temperature change is crucial, as it can affect the rate and direction of chemical reactions, product formation, and safety. For example, in exothermic reactions, where heat is released, the temperature increases; in endothermic reactions, which absorb heat, the temperature drops.

Careful measurement of the temperature change helps chemists and engineers optimize conditions for desired reactions. Using a thermometer and applying principles of thermochemistry, you can calculate the amount of energy involved in causing the temperature change. Such calculations are fundamental when determining the enthalpy of a reaction, which is the total heat content of a system.

Thermochemistry Calculations

Thermochemistry is a branch of chemistry that deals with the energy changes associated with chemical reactions and physical transformations. Thermochemistry calculations typically involve equations and formulas that allow scientists to quantify the amount of heat involved in chemical processes.

To perform these calculations, one important formula involves the specific heat capacity (\(c\)), the mass (\(m\)) of the substance, and the change in temperature (\(\text{Δ}T\)). The formula is expressed as \(q = mc\text{Δ}T\), where \(q\) represents the heat transferred, \(m\) is the mass, \(c\) is the specific heat capacity, and \(\text{Δ}T\) is the temperature change. This equation is foundational in calculating how much energy is needed to heat up a substance or released when it cools down.

Detailed understanding of these calculations allows prediction and control over reactions in a laboratory setting, chemical manufacturing, and even in everyday applications such as cooking or climate control. When undertaking these calculations, it's essential to ensure units are consistent and measure quantities accurately, as the correctness of the result hinges on precise data.