Thermodynamics Flashcards
What type of properties are INDEPENDENT of mass?
Intensive Properties
What type of properties are PROPORTIONAL to mass?
Extensive Properties
What type of properties are expressed on a per-mass basis; shown in lowercase?
Specific Properties
For a single-phase pure component, how many intensive, independent properties are required to determine all the rest?
2
When heat is added to a gas at constant volume, we have
Qv = Cv*∆T = ∆U + W = ∆U
because no work is done. Therefore,
dU = Cv*dT and Cv = dU/dT
When heat is added to a gas at constant pressure, we have
When heat is added at constant pressure, we have
Qp = Cp∆T = ∆U + W = ∆U + P∆V
CpdT = dU + PdV = CVdT + PdV
Quality x, for liquid-vapor systems at saturation, is defined as the mass fraction of the vapor phase:
x = m_g / (m_g + m_f)
where
m_g = mass of vapor
m_f = mass of liquid
Two-Phase (Vapor-Liquid) system expressions:
v = xv_g + (1 – x) v_f or v = v_f + xv_fg u = xu_g + (1 – x) u_f or u = u_f + xu_fg h = xh_g + (1 – x) h_f or h = h_f + xh_fg s = xs_g + (1 – x) s_f or s = s_f + xs_fg
where
_f = specific property of saturated liquid
_g = specific property of saturated vapor
_fg = specific property change upon vaporization = vg – vf
Ideal Gas Law
Pv = RT or PV = mRT and P1v1/T1 = P2v2/T2
where P = pressure v = specific volume m = mass of gas R = gas constant T = absolute temperature V = volume
Gas constant, R
R is specific to each gas but can be found from
R = R_ / (mol wt)
where R_ = universal gas constant
For ideal gases, Cp – Cv = R
For cold air standard, heat capacities are assumed to be constant at their room temperature values. In that case, the following are true:
∆u = Cv∆T; ∆h = Cp ∆T ∆s = Cp ln (T2 /T1) – R ln (P2 /P1) ∆s = Cv ln (T2 /T1) + R ln (v2 /v1)
Also, for constant entropy processes:
(P2/P1) = (v1/v2)^k (T2/T1) = (P2/P1)^((k-1)/K) (T2/T1) = (v1/v2)^(k-1_
where:
k = Cp/Cv
Mole Fraction of an Ideal Gas Mixture (xi)
where:
i = 1, 2, …, n constituents. Each constituent is an ideal gas.
Ni = number of moles of component i
N = total moles in the mixture
xi = Ni/N
N = ΣNi
Σxi = 1
Mass Fraction of an Ideal Gas Mixture (yi)
where:
i = 1, 2, …, n constituents. Each constituent is an ideal gas.
yi = mi/m
m = Σmi
Σyi = 1
Molecular Weight of an Ideal Gas (M)
M = m/N = ΣxiMi
To convert mole fractions (xi) to mass fractions (yi):
yi = xiMi / ΣxiMi
To convert mass fractions to mole fractions:
xi = yi/Mi / Σyi/Mi
Partial Pressures & Volumes of an Ideal Gas:
where:
P, V, T = pressure, volume, and temperature of the mixture
Ri = R/Mi
Pi = miRiT / V and P = ΣPi
Vi = miRiT / P and V = ΣVi
Expressions of Internal energy (u), enthalpy (h), and entropy (s) for mole fractions can be evaluated at:
ui and hi are evaluated at T
si is evaluated at T and Pi
Compressibility Factor
The generalized compressibility chart provides reasonable estimates for the compressibility factor Z based on dimensionless reduced pressure P_R and reduced temperature T_R.
Where, P_C and T_C are the critical pressure and temperature respectively expressed in absolute units.
P_R = P / P_C T_R = T / T_C
Equations of state (EOS) are used to quantify PvT behavior.
For ideal gas EOS (applicable only to ideal gases):
P = (RT / v)
For generalized compressibility EOS (applicable to all systems as gases, liquids, and/or solids):
P = (RT / v) * Z
What are the (3) types of thermodynamic systems?
Open
Closed
Isolated
An OPEN system can exchange both energy and matter with its surroundings. The stovetop example would be an open system, because heat and water vapor can be lost to the air.
A CLOSED system, on the other hand, can exchange only energy with its surroundings, not matter. If we put a very tightly fitting lid on the pot from the previous example, it would approximate a closed system.
An ISOLATED system is one that cannot exchange either matter or energy with its surroundings. A perfect isolated system is hard to come by, but an insulated drink cooler with a lid is conceptually similar to a true isolated system. The items inside can exchange energy with each other, which is why the drinks get cold and the ice melts a little, but they exchange very little energy (heat) with the outside environment.
What are the components of a thermodynamic universe?
A SYSTEM and its SURROUNDINGS, separated by a BOUNDARY.
What is the 1st Law of Thermodynamics?
aka the Law of Conservation of Energy
The net energy crossing the system boundary is equal to the change in energy inside the system.
“energy can neither be created nor destroyed; energy can only be transferred or changed from one form to another”
HEAT, Q (q = Q/m), is energy transferred due to temperature difference and is considered positive if it is inward or added to the system.
WORK, W (w = W/m), is considered positive if it is outward or work done by the system.
Closed Thermodynamic System
No mass crosses the system boundary: Q – W = ∆U + ∆KE + ∆PE where ∆U = change in internal energy ∆KE = change in kinetic energy ∆PE = change in potential energy
Special Cases of Closed Systems (With No Change in Kinetic or Potential Energy)
Constant system pressure process (Charles’s Law):
w_b = P∆v
T/v = constant for ideal gas
Special Cases of Closed Systems (With No Change in Kinetic or Potential Energy)
Constant volume process:
w_b = 0
T/P = constant for ideal gas
Special Cases of Closed Systems (With No Change in Kinetic or Potential Energy)
Isentropic process:
where:
Pv^k = constant for ideal gas
w = (P2v2 - P1v1) / (1-k) = R(T2-T1) / (1-k)
Special Cases of Closed Systems (With No Change in Kinetic or Potential Energy)
Constant temperature process (Boyle’s Law):
where:
P_v = constant for ideal gas
w_b = RTln(v2/v1) = RTln(P1/P2)
Special Cases of Closed Systems (With No Change in Kinetic or Potential Energy)
Polytropic process:
where:
Pv^n = constant for ideal gas
where n is the polytropic exponent or polytropic index
w = (P2v2 - P1v1) / (1-n)
n does not equal 1
Open Thermodynamic Systems
Mass does cross the system boundary. Flow work (Pv) is done by mass entering the system.
The reversible flow work can be expressed:
w_rev = – ⌠vdP + ∆KE + ∆PE
The First Law applies whether or not processes are reversible.
Open System First Law (energy balance):
d(m_s,u_s)/dt = Σmi(hi + ((Vi^2) / 2) + gZi) - Σme(he + ((Ve^2) / 2) + gZe) + Q_in - W_net
where m = mass flow rate (subscripts i and e refer to inlet and exit states of system) g = acceleration of gravity Z = elevation V = velocity ms = mass of fluid within the system us = specific internal energy of system Qin = rate of heat transfer (ignoring kinetic and potential energy of the system) Wnet = rate of net or shaft work
Special Cases of Open Systems (With No Change in Kinetic or Potential Energy)
Constant volume process:
w_rev = – v (P2 – P1)
Special Cases of Open Systems (With No Change in Kinetic or Potential Energy)
Constant system pressure process:
w_rev = 0
Special Cases of Open Systems (With No Change in Kinetic or Potential Energy)
Constant temperature process:
Pv = constant for ideal gas
w_rev = RTln(v2/v1) = RTln(P1/P2)
