Question

The specific internal energy is arbitrarily set to zero in Table A-2 for saturated liquid water at \(0.01^{\circ} \mathrm{C}\). If the reference value for \(u\) at this reference state were specified differently, would there be any significant effect on thermodynamic analyses using \(u\) and \(h\) ?

Short answer

Changing the reference value for specific internal energy does not significantly affect thermodynamic analyses, as these analyses rely on differences in values, which remain unchanged.

Step-by-step solution

Understand the Specific Internal Energy Reference

The specific internal energy, denoted as u, can be set to a reference value for convenience. In Table A-2, this value is set to zero for saturated liquid water at 0.01°C.

Identify the Reference State

The reference state is a chosen state where properties like specific internal energy (u) are set to a defined value. This is a common practice in thermodynamics to standardize tables and calculations.

Consider Different Reference Values

If the reference value for u at the reference state (0.01°C) were specified differently, it would alter the absolute values of specific internal energy, u, throughout the table. However, it would not change the relative differences between u values at other states.

Effect on Thermodynamic Analyses

Thermodynamic analyses often rely on differences in u and h (specific enthalpy). As long as these differences remain unchanged, the analyses and results remain consistent. Hence, choosing a different reference value for u does not significantly affect thermodynamic analyses.

Key concepts

Reference State

In thermodynamics, a reference state is a predefined condition or set of conditions where properties like specific internal energy (u) are assigned set values.

For instance, in many tables, the specific internal energy for saturated liquid water is often set to zero at 0.01°C. This arbitrary setting helps standardize values and make calculations easier.

By convention, picking a reference state is a common practice for consistently tabulating thermodynamic properties. Changing this reference point alters the absolute values but doesn't affect the differences between values. These differences are what matter most in practical calculations.

Thermodynamic Analysis

Thermodynamic analysis involves examining how energy is exchanged within a system. Key properties such as specific internal energy (u) and specific enthalpy (h) play crucial roles.

The effectiveness of thermodynamic calculations relies on relative changes in these properties. By focusing on differences rather than absolute values, analyses remain consistent regardless of the reference state.

Therefore, even if the reference value for u changes (e.g., setting it differently than zero at 0.01°C), it won't significantly impact the outcomes of the thermodynamic analysis.

Specific Enthalpy

Specific enthalpy (h) is a property used in thermodynamic calculations, representing the total energy of a system per unit mass. It includes both the internal energy (u) and the product of pressure (P) and volume (V), given by the formula: 𝒉 = 𝒖 + 𝑷𝑽. This equation means that specific enthalpy takes into account both the energy stored within the fluid and the energy required to displace its surroundings.

Like specific internal energy, specific enthalpy's absolute value depends on the reference state. However, the analyses focus on changes in enthalpy (∆h), not absolute values. Thus, choosing a different reference state does not significantly influence the outcomes based on enthalpy differences.

Whether analyzing heating, cooling, or phase change processes, understanding the role of specific enthalpy and its reliance on the reference state is key to accurate thermodynamic analysis.