Closed Systems

What is moving boundary work?

Moving boundary work, often referred to as boundary work or PdV work, is the type of work performed due to the movement of the boundary of a control volume, typically seen in engines or compressors. It arises when a gas expands or compresses against a piston, resulting in a change of volume, which directly correlates to the pressure exerted by the gas.

What is the main equation for differential work in a moving boundary work scenario?

The differential work (δWb) done as the piston moves can be quantified by the equation: δWb = F ds, where F is the force exerted and ds is the distance moved by the piston. When expressed in terms of pressure and volume, it simplifies to δWb = PA ds = P dV, linking force with pressure and the corresponding change in volume.

What does the energy balance for a closed system express?

The energy balance for any closed system is articulated as: Ein - Eout = ΔEsystem, illustrating that the total energy entering a system minus the energy leaving the system equals the change in the energy of the system. This fundamental principle ensures that energy is conserved within the closed boundaries.

What are the two main types of specific heat?

Specific heat comes in two primary forms: specific heat at constant volume (cv), which measures the heat required to raise the temperature of a unit mass without changing its volume, and specific heat at constant pressure (cp), which measures the heat required to increase the temperature of a unit mass under constant pressure conditions.

What is the relationship between specific heats at constant pressure and constant volume for a given substance?

For any given substance, it is established that the specific heat at constant pressure (cp) is always greater than that at constant volume (cv). This difference arises because when heating at constant pressure, additional energy is required for the substance to perform work against the external pressure.

How can the changes in internal energy (Δu) and enthalpy (Δh) of an ideal gas be calculated?

For an ideal gas, changes in internal energy (Δu) and enthalpy (Δh) can be calculated using the integrals: Δu = u2 - u1 = ∫T1 T2 cv(T) dT for internal energy changes, and Δh = h2 - h1 = ∫T1 T2 cp(T) dT for enthalpy changes, where cv(T) and cp(T) are the specific heats that can be functions of temperature.

What is the equation that relates cp and cv for ideal gases?

For ideal gases, the relationship between specific heats is given by the equation: cp = cv + R, where R is the ideal gas constant. This relationship highlights how Cp incorporates the effect of work done in expansion at constant pressure.

How do specific heats behave in incompressible substances?

In the case of incompressible substances, the specific heats equate to one value, expressed as: cp = cv = c. This single specific heat value suffices because the volume does not change significantly with pressure, simplifying calculations in thermodynamic analyses.

In a closed system undergoing a cycle, what simplifies the energy balance equation?

In a closed system undergoing a complete thermodynamic cycle, the change in internal energy over one complete cycle is zero (ΔEsystem = 0). As such, the energy balance simplifies to: Ein = Eout, indicating that all energy entering the system equals the energy exiting it during the cycle.

What additional approximation can be made for specific heat over small temperature ranges?

For small changes in temperature, specific heat can often be treated as constant, which simplifies calculations. Thus, approximations can be made as Δu = cv,avg (T2 - T1) and Δh = cp,avg (T2 - T1), where cv,avg and cp,avg are the average specific heats over the temperature range in question.