a. How much energy is needed to raise the temperature of a 75 g sample of aluminum from 22.4°C to 94.6°C?

Introduction:

Understanding the amount of energy required to change the temperature of a substance is fundamental in many fields, from chemistry and physics to engineering and everyday applications. In this case, we're looking at how much energy it takes to heat a 75 g sample of aluminum.

Specific Heat Capacity of Aluminum:

To determine the energy required, we first need to consider the specific heat capacity of aluminum. The specific heat capacity (c) is a unique property of each material and represents the amount of heat energy needed to raise the temperature of 1 gram of that substance by 1 degree Celsius (or 1 Kelvin). For aluminum, the specific heat capacity (c) is approximately 0.897 J/g°C (joules per gram per degree Celsius).

Mass of the Sample:

The next piece of the puzzle is the mass of the aluminum sample. You mentioned that it's 75 grams, so we'll use that value in our calculations.

Change in Temperature:

We're looking to raise the temperature of the aluminum from 22.4°C to 94.6°C. To find the change in temperature (ΔT), we subtract the initial temperature from the final temperature:

ΔT = 94.6°C - 22.4°C = 72.2°C

Calculating the Energy:

Now, we can use the specific heat capacity formula to calculate the energy (Q) needed to raise the temperature of the aluminum sample:

Q = m * c * ΔT

Where:

Q is the energy in joules (J).

m is the mass of the sample (75 g).

c is the specific heat capacity of aluminum (0.897 J/g°C).

ΔT is the change in temperature (72.2°C).

Plugging in these values:

Q = 75 g * 0.897 J/g°C * 72.2°C

Q ≈ 4863.15 J

Conclusion:

Therefore, approximately 4863.15 joules of energy are needed to raise the temperature of a 75 g sample of aluminum from 22.4°C to 94.6°C. This calculation is essential in various scientific and practical applications, from cooking to materials engineering, and helps us understand the energy requirements for temperature changes in different substances.