Question

The "Chemistry in Focus" segment Nature Has Hot Plants discusses thermogenic, or heat-producing, plants. For some plants, enough heat is generated to increase the temperature of the blossom by 15 C. About how much heat is required to increase the temperature of 1 L of water by 15 " \(\mathrm{C}\) ?

Short answer

It takes approximately 9405 Joules of heat to increase the temperature of 1 L of water by 15°C. This is calculated using the formula \(q = mcΔT\), where \(m = 1\, kg\) (mass of water), \(c = 4.18\,J/(g\cdot °C)\) (specific heat capacity of water), and ΔT = \(15\,°C\) (change in temperature).

Step-by-step solution

Convert volume to mass

Since the density of water is 1 g/mL, we can easily convert the volume of water given (1 L) to mass in grams: 1 L = 1000 mL Mass of water = 1000 mL * 1 g/mL = 1000 g Now, convert the mass to kg: Mass of water = 1000 g * (1 kg / 1000 g) = 1 kg

Calculate the change in temperature

The change in temperature, ΔT, is already given in the problem as 15°C.

Use the formula for heat transfer

We can now use the formula for heat transfer to find the amount of heat required to increase the temperature of 1 L of water by 15°C: \(q = mcΔT\) where: - \(q\) is the heat required - \(m = 1\, kg\) (mass of water) - \(c = 4.18\,J/(g\cdot °C)\) (specific heat capacity of water) - ΔT = \(15\,°C\) (change in temperature)

Calculate the heat required

Now, we can plug in the values into the formula: \(q = (1\,kg) \times (4.18\,J/(g\cdot °C)) \times (15\,°C)\) \(q = 62.7\, J/°C \times 15\,°C\) \(q = 9405\, J\) So, it takes approximately 9405 Joules of heat to increase the temperature of 1 L of water by 15°C.

Key concepts

Understanding Thermogenic Plants

Thermogenic plants exhibit a fascinating biological phenomenon where they can generate heat, often to attract pollinators. These plants have a specialized mechanism that allows them to produce heat by burning stored energy substances, such as fats or carbohydrates, a process akin to the metabolic activities in warm-blooded animals.

For instance, the skunk cabbage can produce temperatures around 15 to 35 degrees Celsius above the ambient temperature, even in snow. This heat can play a crucial role in the plant's life cycle, not only by enticing pollinators with warm and comfortable conditions but also by helping to spread its scent further afield, which improves its chances of reproduction.

Such biological heat generation can be understood through principles of chemistry, where energy transformations are quintessential. The amount of heat generated by such plants can be significant enough to change the temperature of their surroundings, a concept directly linked to the amount of energy or heat required to change the temperature of a substance, such as water.

Specific Heat Capacity

The concept of specific heat capacity is crucial when calculating the amount of heat needed to change the temperature of a substance. It is defined as the amount of heat required to raise the temperature of one gram of a substance by one degree Celsius. Water, for example, has a high specific heat capacity of about 4.18 J/(g·°C), which means it can absorb a lot of heat before its temperature rises significantly.

This property of water has important implications in both nature and technology. For example, it's one of the reasons why water is an excellent coolant and why the Earth's oceans influence climate by storing and distributing heat. In the context of thermogenic plants, understanding specific heat capacity helps us quantify the amount of energy they release to raise the temperature of their surroundings. The exercise demonstrates how to calculate the heat transfer using water's specific heat capacity, which provides a common reference for energy transformations in biological systems.

Enthalpy Calculations

Enthalpy is a measure of the total heat content of a system and is essential in thermodynamics and chemistry for understanding energy changes during chemical reactions and physical processes.

In the textbook example, the enthalpy change, or the amount of heat required to increase the temperature of water by 15°C, is calculated using the formula: \[q = mcΔT\]
Here, 'q' represents the heat involved in the process, 'm' is the mass of water, 'c' stands for the specific heat capacity of the substance, and 'ΔT' is the change in temperature. This formula is a simplified expression of the enthalpy change for situations where pressure remains constant.

Calculating the enthalpy allows us to understand the heat exchange involved in a given process, making it a key concept in many areas of science, especially in studying thermal properties of plants like thermogenic plants, as well as in various practical applications including heating systems and culinary arts. It helps scientists and engineers design systems for efficient energy utilization and conservation.