C20 - 1st Law of Thermodynamics

E_int

all energy related to microscopic functions within a system

R constant

R = 8.314 (J)/(mol•K)

R = 8.314 (Pa•m³)/(mol•K)

R= 0.0821 (L•atm)/(mol•K)

Heat

transfer of energy between high temperature and low temperature areas of a system

Calorie

energy required to +1ºC to 1g H₂O_(l)

• 1 calorie = 4.186 J

heat capacity

C = Q/∆T

specific heat

c = Q/m∆T

• Q = mc∆T

Latent heat

L = Q/∆m

• ∆m = change in mass of higher-phase substance

Latent heat types

L_vaporization = latent energy for vaporization (liquid → gas)

L_fusion = latent energy for (solid → liquid)

• reverse processes are equal in magnitude & opposite in sign (-L)

Work done on a gas (closed environment)

1st Law of Thermodynamics

∆E_int = Q + W

• cyclic: Q + W = 0

• adiabatic: ∆E_int = W

• isovolumetric: ∆E_int = Q

• isobaric: W = -P(V_f - V_i)

isotherm (work done)

conduction between two faces of block mass

P = kA(∆T/∆x) = kA|dT/dx|

conduction between two ends of a rod

P = kA(∆T/L) = A(∆T/R)

conduction between two ends of a rod (multiple materials)

P = kA(∑(∆T_i/L_i)) = A(∆T/∑R_i)

temperature gradient

Stefan’s Law

Q_radiated = σeAT⁴

Q_net = σeA(T⁴ - (T₀)⁴)

• σ = 5.7 × 10^-8 W/(m² • K⁴)

• e = emissivity = absorptivity (0 < e < 1)

• A = surface area

• T₀ = ambient temperature

types of transfer mechanisms

• conduction (Q)

• convection (T_MT)

• radiation (T_ER)

L_v (H₂O)

2.26 × 10⁶ J/kg

L_f (H₂O)

3.33 × 10⁵ J/kg

c (H₂O)

4186 J/(kg • ºC)

conservation of energy (isolated heat transfer)

Q_cold = -Q_hot

• Q_cold = energy entering the cold substance (+)

• Q_hot = energy leaving the hot substance (-)

Stefan-Boltzmann constant

σ = 5.7 × 10^-8 W/(m² • K⁴)

Pa → atm

1 atm = 101325 Pa

m³ → L

1 m³ = 1000 L