Energy Balance and Concentration Dynamics

Vocabulary flashcards reviewing key concepts, mathematical definitions, and mass balance principles covered in the lecture transcript.

Well-Mixed Assumption

A classical modeling assumption that the salt concentration throughout the liquid inside a tank is completely uniform at any given moment.

Initial Tank Salt Concentration

The salt concentration in the tank at time $t = 0$, calculated as $2\,\text{kg}$ of salt divided by $40\,\text{L}$ of liquid, which equals $0.05\,\text{kg\,L}^{-1}$.

Inlet Salt Concentration

The constant salt concentration of the incoming fluid stream, specified as $0.3\,\text{kg\,L}^{-1}$.

Concentration Gap

The numerical difference between the inlet salt concentration and the tank salt concentration, which drives the exponential rate of concentration change over time.

Mass Balance Case 1

A system state where mass input ($1\,\text{kg\,s}^{-1}$) equals mass output ($1\,\text{kg\,s}^{-1}$), resulting in zero net change of mass within the system boundary.

Mass Balance Case 2

A system state where mass input ($2\,\text{kg\,s}^{-1}$) exceeds mass output ($1\,\text{kg\,s}^{-1}$), resulting in a net mass accumulation of $1\,\text{kg\,s}^{-1}$ inside the system boundary.

Mass Balance Case 3

A system state where mass output ($5\,\text{kg\,s}^{-1}$) exceeds mass input ($2\,\text{kg\,s}^{-1}$), resulting in a net mass reduction of $3\,\text{kg\,s}^{-1}$ inside the system boundary.

Governing Differential Equation

An ordinary differential equation (ODE) formulated from mass balance principles to describe the continuous time-dependent rate of change of salt mass inside the tank.

Tank Filling Duration

The time required to fill an empty $40\,\text{L}$ tank at a volume flow rate of $0.15\,\text{L\,s}^{-1}$, calculated as approximately $266.67\,\text{s}$.

Steady-State Salt Mass

The maximum upper bound of salt mass in the $40\,\text{L}$ tank as time approaches infinity, calculated as $0.3\,\text{kg\,L}^{-1} \times 40\,\text{L} = 12\,\text{kg}$.