Question

Explain why you need to know the specific heat of a substance in order to calculate how much heat is gained or lost by the substance as a result of a temperature change.

Short answer

Knowing the specific heat of a substance is essential for calculating the heat gained or lost due to a temperature change because it is a fundamental factor in the heat transfer formula, \(Q = mcΔT\), where Q is the heat gained or lost, m is the mass, c is the specific heat, and ΔT is the temperature change. Specific heat determines the amount of heat needed to change the temperature of a substance; different substances have different specific heats. Understanding specific heat allows us to estimate and control the heat needed for various processes and design materials with optimal heat transfer properties.

Step-by-step solution

Define specific heat

Specific heat (often denoted by "c" or "Cp" for constant-pressure specific heat) is a property of a substance that determines the amount of heat required to change its temperature by a certain amount. It is usually expressed in units of joules per kilogram per degree Celsius (J/kg·°C) or calories per gram per degree Celsius (cal/g·°C). Different substances have different specific heats, which means they require different amounts of heat to change their temperature.

Explain heat transfer in relation to specific heat

Heat transfer occurs when there is a difference in temperature between two substances or between different parts of a single substance. The amount of heat transferred depends on the mass, specific heat, and temperature difference of the substances involved. For example, if you heat a pot of water on a stove, the heat from the stove is transferred to the water, causing its temperature to rise. The specific heat of water determines how much heat it can absorb and how quickly its temperature will increase.

Introduce the formula for heat transfer

The formula for heat transfer (Q) in relation to specific heat (c), mass (m), and temperature change (ΔT) is given by: \[Q = mcΔT\] where: - Q is the heat gained or lost by a substance (in joules or calories) - m is the mass of the substance (in kilograms or grams) - c is the specific heat of the substance (in J/kg·°C or cal/g·°C) - ΔT is the change in temperature of the substance (in °C)

Explain the importance of specific heat in the formula

From the formula, we can see that specific heat (c) is one of the factors that determine the amount of heat (Q) gained or lost by a substance due to temperature change. If we know the mass, specific heat, and temperature change of a substance, we can calculate how much heat is required to achieve the desired temperature change. Knowing the specific heat of a substance is important because it allows us to estimate the amount of heat needed for various processes, such as heating or cooling, as well as evaluating the efficiency of heat transfer systems. It also helps scientists and engineers design materials with optimal heat transfer properties for specific applications.

Key concepts

Heat Transfer

Understanding heat transfer is crucial when it comes to many aspects of science and engineering, including when we want to increase or decrease the temperature of a substance. Heat transfer is a phenomenon that occurs when there is a temperature difference between two objects or systems. The heat will naturally flow from the hotter object to the cooler one until thermal equilibrium is reached, meaning both objects are at the same temperature.

For instance, if you leave a metal spoon in a hot cup of coffee, after some time, the spoon gets warmer. This is because heat is transferring from the hot coffee to the cooler spoon. The rate at which this heat transfer occurs depends on several factors, including the properties of the substance through which the heat is flowing. In the case of the spoon, its conductivity and mass play a role, along with how much hotter the coffee is than the spoon.

Various everyday phenomena, from cooking food on a stove to the functioning of a car's radiator, involve heat transfer. Understanding how heat moves from one place to another enables us to control and utilize this energy for our benefit, whether it's to keep our houses warm or to design more efficient engines.

Temperature Change

When we talk about temperature change, we're referring to the variation of a substance's temperature, which can occur as a result of heat transfer. The temperature of a substance increases when it absorbs heat and decreases when it loses heat. How rapidly this temperature change happens is a characteristic of the material itself, represented by its specific heat.

If we consider a container of water being heated on a stovetop, the water's temperature will rise over time as heat is transferred from the burner to the water. The specific heat of water tells us that it requires 4.186 joules to raise the temperature of one gram of water by one degree Celsius. This property makes it a good substance for temperate regulation, such as in radiators or as a coolant in engines.

Temperature change is not always linear and can be affected by the environment, such as the presence of insulation or the relative humidity of the air. These additional factors could slow down or speed up the rate at which a substance changes temperature and must be considered in practical applications.

Heat Transfer Formula

One of the essential formulas in understanding how heat energy is moved or stored within an object is the heat transfer formula. It quantitatively describes how much energy is needed to change the temperature of a given mass of a substance. The formula is written as:

\[Q = mcΔT\]
Where Q stands for the heat absorbed or released, m is the mass of the substance, c represents the specific heat capacity, and ΔT is the change in temperature.

This formula is invaluable because it allows us to calculate the quantity of energy transfer required to achieve a specific temperature change in a material. For example, if you want to heat a pool of water, knowing the mass of the water, the desired temperature increase, and the specific heat capacity of water allows you to determine the amount of energy, in the form of heat, necessary to reach that temperature change.

Furthermore, the formula helps design systems by enabling engineers to estimate how much fuel or energy would be required to achieve desired heating or cooling effects, making it a cornerstone in thermal management and energy conservation strategies.