Question

The quantity of energy required to change the temperature of a sample is calculated by taking the product of the mass of the sample, the specific heat capacity of the sample, and the ____ change undergone by the sample.

Short answer

The missing word is "temperature." The quantity of energy required to change the temperature of a sample is calculated by taking the product of the mass of the sample, the specific heat capacity of the sample, and the temperature change undergone by the sample.

Step-by-step solution

Identify the energy transfer formula

The missing word in the exercise can be found by recalling the formula for the energy transfer involved in changing the temperature of a sample. The formula is given by: \(q = mc\Delta T\) where - q represents the energy required for the temperature change - m represents the mass of the sample - c represents the specific heat capacity of the sample - \(\Delta T\) represents the change in temperature

Understand the meaning of the variables in the formula

To find the missing word in the given exercise, let's understand the meaning of the variables in the energy transfer formula (\(q = mc\Delta T\)): - q: The energy required to change the temperature of the sample - m: The mass of the sample - c: The specific heat capacity of the sample, which is a measure of the amount of energy required to raise the temperature of 1 gram of the substance by 1 degree Celsius - \(\Delta T\): The change in temperature that the sample undergoes Here, the missing word should describe the variable that represents the physical property involved in the relationship.

Identify the missing word in the given sentence

Based on the energy transfer formula and the meaning of the variables, the missing word in the given exercise is "temperature." Now we can complete the sentence: The quantity of energy required to change the temperature of a sample is calculated by taking the product of the mass of the sample, the specific heat capacity of the sample, and the temperature change undergone by the sample.

Key concepts

Energy Transfer Formula

To determine how much energy is needed to change the temperature of a sample, we use an important equation known as the energy transfer formula. This formula, written as \(q = mc\Delta T\), helps calculate the quantity of heat energy \(q\) required. Here's what each part of this formula represents:

• \(q\): Refers to the heat energy needed to cause the temperature change.
• \(m\): Denotes the mass of the sample in question.
• \(c\): Represents the specific heat capacity of the sample.
• \(\Delta T\): Indicates the change in temperature the sample undergoes.

By multiplying the mass of the sample, its specific heat capacity, and the temperature change it undergoes, we can calculate the total energy transfer. This formula is crucial in thermodynamics and helps in understanding how different materials absorb and transfer energy.

Temperature Change

When using the energy transfer formula, one of the key variables to consider is the change in temperature, represented as \(\Delta T\). This variable is critical because it highlights how much the sample's temperature increases or decreases.

The change in temperature is calculated by subtracting the initial temperature from the final temperature. So, the formula for temperature change is:\[\Delta T = T_{\text{final}} - T_{\text{initial}}\]In this equation:

• \(T_{\text{final}}\): The temperature of the sample after the energy transfer.
• \(T_{\text{initial}}\): The temperature before the energy input.

A positive \(\Delta T\) signifies a temperature increase, whereas a negative value indicates a decrease. This measurement is important as it directly relates to the amount of energy needed for the temperature change, as outlined in the energy transfer formula.

Mass of the Sample

Another critical component in the energy transfer formula is the mass of the sample. Represented as \(m\) in the formula \(q = mc\Delta T\), this quantity plays a significant role in determining the amount of energy a substance can absorb or lose during thermal processes.
Why is mass important? Here are a few reasons:

• The larger the mass of the sample, the greater the amount of energy needed to change its temperature. A heavier object will require more energy to heat or cool compared to a lighter one.
• Mass helps in calculating the energy distributed per unit of material, providing insights into how the material will respond to energy transfer.

In practical settings, knowing the exact mass of the sample allows scientists and engineers to predict and control energy needs during experiments and industrial processes.