What is the entropy change of the nitrogen if 250 mL of liquid nitrogen boils away and then warms to 20℃ at constant pressure? The density of liquid nitrogen is 810 kg/m³.

검증된 단계별 안내

Step 1: Calculate the mass of the liquid nitrogen. Use the formula \( m = \rho \cdot V \), where \( \rho \) is the density of liquid nitrogen (810 kg/m³) and \( V \) is the volume (250 mL = 0.00025 m³).

Step 2: Determine the entropy change during the phase change (boiling). Use the formula \( \Delta S_{\text{boil}} = \frac{m \cdot L}{T_{\text{boil}}} \), where \( L \) is the latent heat of vaporization for nitrogen (199 kJ/kg) and \( T_{\text{boil}} \) is the boiling temperature of nitrogen in Kelvin (77 K).

Step 3: Calculate the entropy change as the nitrogen gas warms from its boiling point to 20℃. Use the formula \( \Delta S_{\text{warm}} = m \cdot c_p \cdot \ln\left(\frac{T_{\text{final}}}{T_{\text{initial}}}\right) \), where \( c_p \) is the specific heat capacity of nitrogen gas (1.04 kJ/kg·K), \( T_{\text{final}} \) is 20℃ in Kelvin (293 K), and \( T_{\text{initial}} \) is the boiling temperature (77 K).

Step 4: Add the two entropy changes together to find the total entropy change. Use \( \Delta S_{\text{total}} = \Delta S_{\text{boil}} + \Delta S_{\text{warm}} \).

Step 5: Ensure all units are consistent throughout the calculations (e.g., convert kJ to J where necessary) and verify the final expression for \( \Delta S_{\text{total}} \).

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12m

주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Entropy

Entropy is a measure of the disorder or randomness in a system. In thermodynamics, it quantifies the amount of energy in a physical system that is not available to do work. When a substance undergoes a phase change, such as boiling, its entropy typically increases due to the greater freedom of movement of molecules in the gas phase compared to the liquid phase.

Phase Change

A phase change refers to the transition of a substance from one state of matter to another, such as from liquid to gas. During this process, energy is absorbed or released, which affects the temperature and entropy of the substance. In the case of liquid nitrogen boiling, it absorbs heat from the surroundings, leading to an increase in entropy as it transitions to the gaseous state.

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. For nitrogen gas, this value is crucial when calculating the heat absorbed as the gas warms from its boiling point to a specified temperature, such as 20℃. Understanding this concept allows for the calculation of the total heat transfer and the corresponding change in entropy during the warming process.