Calculate the temperature change that occurs when \(248 \mathrm{cal}\) of heat are added to \(24 \mathrm{~g}\) of water.

Understanding heat transfer is essential when learning about energy and temperature changes in materials. Heat transfer is the process by which thermal energy moves from one body or substance to another. This can occur in three main ways: conduction, in which heat is passed through a solid; convection, where it is carried through liquids and gases; and radiation, which involves heat moving as electromagnetic waves.

When heat transfers to an object, like water in our exercise, it affects the object's temperature. The temperature change depends on several factors, including the amount of heat added, the substance's specific heat capacity, and the mass of the substance being heated. This connection between heat transfer and temperature forms the basis of our exercise in understanding how a specific amount of energy added to water influences its temperature.

Calculating temperature change is a fundamental skill in thermodynamics and a crucial part of our exercise. The temperature change is directly proportional to the amount of heat added or removed from a substance and is inversely proportional to the product of the mass and specific heat capacity of the substance.

As demonstrated in the step-by-step solution, the formula for calculating the change in temperature is: \( \Delta T = \frac{Q}{m \times c} \) where \( \Delta T \) is the temperature change in degrees Celsius (°C), \( Q \) is the heat added or removed in calories (cal), \( m \) is the mass of the substance in grams (g), and \( c \) is the specific heat capacity in calories per gram per degree Celsius (cal/g°C). By using this formula, we can solve practical problems, like finding out how warm our water will get when we add a specific amount of heat.

The calorie is a unit of energy that is commonly used in chemistry and biology to express the amount of heat energy. Specifically, one calorie is defined as the amount of heat required to raise the temperature of one gram of water by one degree Celsius at a pressure of one atmosphere.

In the context of our problem, understanding the calorie unit is important because it helps to quantify the energy involved in heating up a substance. The calorie unit is particularly useful when dealing with biological systems or food energy content, where it is often referred to in kilocalories (kcal), with one kcal representing 1,000 calories. It is crucial to use the correct unit during calculations to ensure accuracy, as mixing up units can lead to errors in determining energy transfer and temperature changes.