(a) Compute the specific heat at constant volume of nitrogen (N2) gas, and compare it with the specific heat of liquid water. The molar mass of N2 is 28.0 g/mol.

Verified step by step guidance

1. Identify the degrees of freedom for nitrogen (N2) gas. As a diatomic molecule, N2 has 5 degrees of freedom at room temperature (3 translational and 2 rotational).
2. Use the formula for specific heat at constant volume for an ideal gas, which is given by $C_v = \frac{f}{2} R$, where $f$ is the degrees of freedom and $R$ is the universal gas constant (approximately 8.314 J/mol·K).
3. Substitute the degrees of freedom for N2 into the formula to calculate $C_v$ for nitrogen gas.
4. Compare the calculated $C_v$ for nitrogen gas with the known value of specific heat of liquid water at constant pressure, which is approximately 4.18 J/g·K.
5. To make a direct comparison, consider converting the specific heat of nitrogen gas from J/mol·K to J/g·K using the molar mass of N2.

Key Concepts

Specific Heat Capacity

Specific heat capacity is the amount of heat required to raise the temperature of a unit mass of a substance by one degree Celsius. It varies for different materials and is crucial for understanding how substances absorb and transfer heat. For gases, specific heat can differ depending on whether the process occurs at constant volume or constant pressure.

Constant Volume vs. Constant Pressure

In thermodynamics, processes can occur at constant volume or constant pressure, affecting the specific heat values. The specific heat at constant volume (Cv) measures how much heat is needed to raise the temperature of a gas without changing its volume, while the specific heat at constant pressure (Cp) accounts for work done by the gas during expansion. For ideal gases, the relationship between Cv and Cp is given by the equation Cp = Cv + R, where R is the gas constant.

Comparison of Specific Heats

Comparing the specific heat of nitrogen gas to that of liquid water highlights the differences in thermal properties between gases and liquids. Water has a high specific heat capacity, which allows it to store and transfer heat effectively, making it essential for climate regulation and biological processes. In contrast, gases like nitrogen typically have lower specific heat capacities, reflecting their lower density and different molecular interactions.