EQUATIONS _ Thermo

The isentropic process relates specific volume and pressure through the equation $T_1 v_1^{k-1} = T_2 v_2^{k-1}$. This shows that specific volume changes with temperature and pressure during an isentropic process.

The work done is calculated using $W = ∫ F ⋅ ds$, where F is the force and ds is the displacement. In terms of pressure-volume work, it can also be expressed as $W = ∫ Pdv$.

Total work done is expressed as $W = m ∫ Pdv$, where m is the mass flow rate. This incorporates mass into the work done over volume change.

<p>The COP is defined as $COP = \frac{q_{in}}{w_{in}}$. It measures the efficiency of a heat pump or refrigerator in converting work input into heat transfer.</p> Signup and view all the answers

<p>Enthalpy is given by the equation $H = U + PV$. This defines how internal energy combines with pressure-volume work to assess total energy in a system.</p> Signup and view all the answers

<p>The equation $du = cv dT$ defines the change in internal energy (du) of a system as a function of its heat capacity at constant volume (cv) and the change in temperature (dT).</p> Signup and view all the answers

<p>$h_x$, $u_x$, and $v_x$ represent the total enthalpy, internal energy, and specific volume of a mixture, respectively, expressed in terms of mass fractions of liquid and vapor. They are calculated as $h_x = h_f + x(h_g - h_f)$, where x is the quality of the vapor.</p> Signup and view all the answers

<p>The relationship is given by $c_p = c_v + R$, indicating that the specific heat at constant pressure is greater than the specific heat at constant volume by the gas constant R.</p> Signup and view all the answers

<p>The Ideal Gas Equation is represented as PV = nRT, where P is pressure, V is volume, n is the number of moles, R is the universal gas constant, and T is temperature.</p> Signup and view all the answers

<p>The specific gas constant for air is R_air = 0.287 kJ/(kg·K), derived from the universal gas constant divided by the molecular weight of air.</p> Signup and view all the answers

<p>In an open system, the mass balance is expressed as dmsys/dt = ∑ṁ_in - ∑ṁ_out.</p> Signup and view all the answers

<p>The energy balance equation for an open system represents the rate of change of energy in the system being equal to the energy in minus the energy out.</p> Signup and view all the answers

<p>The entropy balance for an open system includes contributions from mass flow in and out, along with any entropy generated within the system.</p> Signup and view all the answers

<p>The change in entropy for ideal gases can be calculated using the formula ∆s = C_p ln(T2/T1) - R ln(P2/P1) or ∆s = C_v ln(T2/T1) + R ln(v2/v1.</p> Signup and view all the answers

<p>The term S_gen represents the entropy generation within the system, accounting for irreversible processes.</p> Signup and view all the answers

<p>In closed systems, the expression ΔEsys includes changes in internal energy, kinetic energy, and potential energy, showing the total energy differences.</p> Signup and view all the answers

A thermodynamic process where entropy remains constant. It is characterized by reversible adiabatic changes.

A model used for describing the behavior of ideal gases during isentropic processes. It relates pressure, volume, and temperature using the polytropic index 'k'.

The work done on or by a system due to boundary movement, specifically the expansion or compression of the system's volume.

The work done by a shaft rotating within a system, such as in a turbine or pump.

The rate of work done, either by electrical or mechanical means, expressed in units of power like Watts or horsepower.

The maximum energy efficiency of a thermodynamic cycle, defined as the ratio of useful work output to the heat input.

A measure of how well a heat pump or refrigerator transfers heat, defined as the ratio of heat transferred to work done.

The total enthalpy of a system, which is the sum of its internal energy and the product of pressure and volume.

The ideal gas equation relates pressure, volume, temperature, and the number of moles of an ideal gas. It can be expressed as PV = nRT, where P is pressure, V is volume, n is the number of moles, R is the ideal gas constant, and T is temperature.

The specific gas constant, denoted by R, is a constant specific to each gas. It relates the pressure, volume, mass, and temperature of a gas. The value of R can be found using the universal gas constant and the molecular weight of the gas.

Mass balance is based on the principle of conservation of mass. It states that the mass of a system remains constant over time, even if the system is undergoing changes. In an open system, the mass balance equation takes into account the mass flow rates entering and leaving the system.

Energy balance is based on the principle of conservation of energy. It states that energy cannot be created or destroyed, only transformed from one form to another. In an open system, the energy balance equation accounts for energy transfer rates due to heat transfer, work, and mass flow.

Entropy balance is based on the second law of thermodynamics. It states that the total entropy of an isolated system can never decrease over time. In an open system, the entropy balance equation accounts for the entropy flow rates due to mass transfer, heat transfer, and entropy generation within the system.

Entropy change for an ideal gas can be calculated using various formulas. Some common expressions include: ∆s = Cp ln (T2/T1) - R ln (P2/P1) or ∆s = Cv ln (T2/T1) + R ln (v2/v1). These equations require constant specific heat values.

The specific heat capacity of a substance is a measure of how much heat energy is required to raise the temperature of a unit mass of that substance by one degree. For ideal gases, the specific heat capacity can be constant or variable depending on the thermodynamic process.

The ideal gas constant is a fundamental constant in thermodynamics. It represents the relationship between the pressure, volume, temperature, and the number of moles of an ideal gas. It values approximately 8.314 J/(mol·K) or 0.08206 L·atm/(mol·K).