Bridges are often made of steel and concrete, which expand and contract with temperature changes throughout the year. To prevent the bridge from bending, cracking, or even collapsing, engineers design expansion joints—small gaps between sections of the bridge. These gaps allow the materials to move without causing damage, ensuring the bridge remains safe and functional in all weather conditions.
ΔL=LiΔT
This equation states that under the same temperature, pressure and volume all gases contain the same number of molecules (but not the same mass)
These equations describe processes of finding heat transfer at different constant conditions in the system
Q=nCvΔT
Q=nCpΔT
This equation represents a statistical average of the sum of the squares of the speeds of all gas molecules
Vrms = sq.root (3RT/M)
These conversions help you calculate temperature at different scales
Tc = TK - 273
Tf = 9/5Tc + 32
TK = Tc + 273
In colder climates, the water pipes in buildings are at risk of freezing during winter months. If the pipes are not insulated or if the temperature drops too low, the pressure from the expanding ice can cause the pipes to crack or burst. This not only leads to costly repairs but also results in water damage to the building.
ΔV = Vo β ΔT
These two describe the heat capacity at different constants for gases of single atoms
Cv=(2/3)R
Cp=(5/2)R
γ = Cp/Cv = 5/3
The pressure of the system remains constant
W = -P(Vf-Vi)
This equation describes how to find the change in all the energy within a given system, including the kinetic energy of molecules and the energy stored in all of the chemical bonds between molecules. It is also a law.
ΔU=Q+W or dU = dQ + dW
The change in the degree of disorder or uncertainty in a system. During each step of the transition, the system exchanges heat reversibly at a temperature
Δ𝑆 =ΔQ/T
This equation is used to find the amount of heat transferred per unit mass to raise the temperature of the substance by 1 degree celsius.
These two describe the heat capacity at different constants for gases of 2 atoms
Cv=(5/2)R
Cp=(7/2)R
γ = Cp/Cv = 7/5
The temperature of the system remains constant. For example, keeping hot water in a thermos flask
W= -nRTln(Vf/Vi)
This equation describes how to find the change in all the energy within a monatomic gas system, including the kinetic energy of molecules and the energy stored in all of the chemical bonds between molecules.
ΔU=3/2nRT
This equation explains the change in the degree of disorder or uncertainty in a system when it changes to a different phase
ΔS = mL/T
This equation is used to find the heat required for a substance to change phases
Q = L x m
Which formula represents the relationship between pressure and the average kinetic energy of gas molecules?
P = 2/3 x N/v (1/2 mv2)
No heat is transferred to or from the system
PVγ = const
TVγ-1 = const
This equation describes how to find the maximum productivity of a theoretical cycle proposed by Leonard C.
ε = 1- Tc/Th
This equation explains the change in the degree of disorder or uncertainty in a system with a solid or liquid material
ΔS = mc x ln(Tf/Ti)
The work done by is the difference between the heat absorbed from the hot reservoir and the heat discharged to the cold reservoir
W=Qh−Qc
(Not on formula sheet) These two laws state: 1. At constant temperature, the pressure of a given mass of gas varies inversely with volume, and 2. At constant pressure, the volume of the gas is proportional to its absolute temperature
Boyle's law and Charles Law
Not on the formula sheet: This is a thermodynamic process where the entropy of the system remains constant
Isentropic
This equation describes a ratio that measures the efficiency of a system's ability to provide heating or cooling relative to the amount of energy it consumes
COPh = |Qh|/W
COPc = |Qc|/W
This equation describes how to find the change in the degree of disorder or uncertainty in the state of a hypothetical ideal gas.
ΔS = nCv x ln(Tf/Ti) + nR x ln(Vf/Vi)