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. First, understand that the specific heat at constant volume (C_v) for a gas can be calculated using the formula: $C\_v=\frac{3R}{2}$, where R is the universal gas constant, approximately 8.314 J/(mol·K).
2. Calculate the specific heat at constant volume for nitrogen gas using the formula: $C\_v=\frac{3\times 8.314}{2}$. This will give you the value in J/(mol·K).
3. Next, convert the specific heat from J/(mol·K) to J/(g·K) for nitrogen gas. Use the molar mass of nitrogen, which is 28.0 g/mol, with the formula: $C\_v=\frac{C}{\_}28.0$.
4. For comparison, recall that the specific heat of liquid water is approximately 4.18 J/(g·K). This is a standard value that can be used for comparison purposes.
5. Finally, compare the specific heat of nitrogen gas in J/(g·K) with that of liquid water. Discuss the differences in specific heat values and consider the implications for energy storage and transfer in these substances.

Key Concepts

Specific Heat Capacity

Specific heat capacity is the amount of heat required to change the temperature of a unit mass of a substance by one degree Celsius. It is a crucial property for understanding how different materials absorb and transfer heat. For gases, specific heat can be measured at constant volume or constant pressure, affecting how energy is stored in the substance.

Molar Mass

Molar mass is the mass of one mole of a substance, typically expressed in grams per mole (g/mol). It is essential for converting between the mass of a substance and the amount in moles, which is necessary for calculating specific heat capacities in terms of molar quantities. For nitrogen gas (N2), the molar mass is 28.0 g/mol, which helps in determining its specific heat.

Comparison of States of Matter

Comparing the specific heat of gases and liquids involves understanding the differences in molecular interactions and energy storage. Gases, like nitrogen, have molecules that are more free to move, while liquids, like water, have stronger intermolecular forces. This affects their specific heat values, with liquids generally having higher specific heat due to the energy required to overcome these forces.