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In understanding heat transfer in gases, it's important to consider the concept of ideal gas behavior. An ideal gas is a theoretical gas composed of many randomly moving point particles that interact only through elastic collisions. These gases follow a simple set of rules outlined in the ideal gas law, which is given by the equation \( PV = nRT \), where:

• \( P \) is the pressure of the gas.
• \( V \) is the volume of the gas.
• \( n \) is the number of moles of the gas.
• \( R \) is the ideal gas constant, approximately 8.314 J/mol·K.
• \( T \) is the temperature of the gas.

Assuming a gas behaves ideally means assuming it follows these laws under most conditions, not being influenced by the volume of the particles themselves or any intermolecular forces. This assumption simplifies calculations such as determining heat capacity or amount of heat required for temperature changes in gases. For the exercise, assuming that argon behaves as an ideal gas allows us to use standard formulas to find the heat needed to raise its temperature.

The molar heat capacity of a substance indicates how much heat is required to raise the temperature of one mole of the substance by one Kelvin. For gases, it's often convenient to consider the heat capacity at constant pressure (\( C_p \)). For monatomic gases like argon, \( C_p \) is known to be \( \frac{5}{2}R \). Given \( R \) is 8.314 J/mol·K, we find:

• \( C_p = \frac{5}{2} \times 8.314 \approx 20.785 \text{ J/mol K} \)

This value is broadly applicable to all monatomic gases behaving ideally under similar conditions. Understanding \( C_p \) is crucial for determining how much heat energy is required to effect a temperature change under constant pressure conditions, as the heat required is given by \( Q = nC_p\Delta T \). This helps comprehend the energy dynamics involved in practical applications like heating gases in industrial processes.

Calculating the number of moles is a fundamental step in solving many problems related to gases, including heat transfer. Moles are a measure of quantity that relates directly to the atomic or molecular scale of the substance. For argon, due to its atomic mass of 39.9 grams per mole, we can determine the number of moles present in a given mass using the formula:

• \( n = \frac{\text{mass of the substance}}{\text{molar mass}} \)
• In the exercise, \( n = \frac{8}{39.9} \approx 0.2005 \text{ moles} \)

This calculation is essential because it links the macroscopic measurements of mass and energy to the molecular scale through the ideal gas law and thermodynamic equations. It's a foundational element for being able to further determine energy transfers and transformations, such as heating, in gas systems.

When examining how temperature change affects a gas, especially in the context of heat transfer, it's vital to understand how energy relates to thermal changes. The change in temperature (\( \Delta T \)) directly determines the amount of heat energy required to increase that temperature, calculated using the formula \( Q = nC_p\Delta T \).

• \( \Delta T \) represents the change in temperature, which in this scenario is 75 K.
• \( Q \) is the heat added or removed.
• \( n \) and \( C_p \) have been previously determined.

With \( C_p \) for argon being 20.785 J/mol·K and \( n \) being 0.2005 moles, the formula allows for computing the heat required as \( Q \approx 312.3 \text{ J} \). Recognizing how temperature alterations impact heat energy surrounds the ability to control and predict thermal processes in gases, crucial for various applications, from scientific research to industrial operations.