Question

What is the heat change when \(55.0 \mathrm{~g}\) of water cools from \(60.0^{\circ} \mathrm{C}\) to \(25.5^{\circ} \mathrm{C}\) ?

Short answer

The heat change when \(55.0 \mathrm{~g}\) of water cools from \(60.0^{\circ} \mathrm{C}\) to \(25.5^{\circ} \mathrm{C}\) is \(7910.3 \mathrm{~J}\)

Step-by-step solution

Identify the given values

The mass (m) of the water is given as \(55.0 \mathrm{~g}\). The temperature changes from an initial temperature (\(T_i\)) of \(60.0^{\circ} \mathrm{C}\) to a final temperature (\(T_f\)) of \(25.5^{\circ} \mathrm{C}\). The specific heat capacity (c) for water is \(4.18 \mathrm{~J/g \cdot \degree C}\).

Calculate the temperature change

Calculate the change in temperature (\(ΔT\)) by subtracting the final temperature from the initial temperature: \(ΔT = T_i - T_f = 60.0^{\circ} \mathrm{C} - 25.5^{\circ} \mathrm{C} = 34.5 \mathrm{~\degree C}\)

Substitute and calculate

Substitute the values of m, c, and \(ΔT\) into the equation for heat change: \(q = mcΔT = 55.0 \mathrm{~g} \times 4.18 \mathrm{~J/g \cdot \degree C} \times 34.5 \mathrm{~\degree C} = 7910.3 \mathrm{~J}\)

Key concepts

Specific Heat Capacity

When it comes to understanding heat change, one of the most important factors is specific heat capacity. This is a property of matter that tells us how much heat energy is needed to raise the temperature of a substance. In simpler terms, it tells you how resistant a material is to changing its temperature. The bigger the specific heat capacity, the more heat is needed.

Consider water, for instance; it has a relatively high specific heat capacity, measured at about 4.18 J/g·°C. This indicates that water can absorb a significant amount of heat before it gets hot. That's why water is often used in cooling systems – because it can store this heat efficiently. For students and learners, always remember that the specific heat capacity is unique to each substance. It directly influences how much heat you'll need or how much heat will be released during a temperature change.

Temperature Change

Understanding temperature change in calculations of heat change is key to solving many problems in thermodynamics and calorimetry. Temperature change is simply the difference between the initial temperature and the final temperature of a system. In mathematical terms, this is expressed as \( \Delta T = T_i - T_f \).

For instance, in a cooling process of water we examined, the initial temperature \( T_i \) might be 60°C and the final temperature \( T_f \) 25.5°C. The temperature change, thus becomes: \( \Delta T = 60.0^{\circ} \mathrm{C} - 25.5^{\circ} \mathrm{C} = 34.5^{\circ} \mathrm{C} \).

Monitoring temperature change is critical because it determines how much heat is absorbed or released. Whenever you're working on problems involving heat change, always calculate your temperature change first. It's an essential step that guides your calculations of heat transfer in various physical operations.

Calorimetry

Calorimetry is the science of measuring heat. In simple words, it's all about figuring out how much energy in the form of heat is moving in or out of a system. Calorimetry applies to changes occurring in chemical reactions, physical changes, and the heating or cooling of substances.

To measure heat changes, a calorimeter is used. This is a device that isolates the reaction or the substance from the surrounding environment to prevent heat exchange with anything else, ensuring accurate measurements.

In the exercise given, calorimetry principles are applied to find the heat lost by water as it cools. Here, the key formula arises from calorimetry itself: \( q = mc\Delta T \), where \( q \) represents the heat change, \( m \) is the mass, \( c \) is the specific heat capacity, and \( \Delta T \) is the temperature change. This formula helps you determine how much heat energy gets transferred during the cooling or heating of a substance, a practical demonstration of the principles of calorimetry.