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Calorimetry Energy Balance

Resultant Temperature of Two Fluid Streams — Adiabatic Mixing Model
This calculator computes the resultant temperature when mixing two fluid streams in the process line using an adiabatic (no heat loss to surroundings) mixing model. It also features a toggle mode for estimation of the mass or mass flow rate required to achieve a desired temperature.
Mode:
User Input
Calculated Output

Fluid Stream 1

STREAM A
kg or kg·hr⁻¹
Supports expressions: 1000−200, 3*150, etc.
kJ / kg·°C
°C

Resultant

Awaiting Input
Final Temperature — Tf
—
°C
Required Mass — m₁
—
kg or kg·hr⁻¹
Total Mass — m₁ + m₂
—
kg or kg·hr⁻¹
°C
Thermal Capacity Ratio
A
B
Stream A
Stream B

Fluid Stream 2

STREAM B
kg or kg·hr⁻¹
Supports expressions: 500+300, 2*750, etc.
kJ / kg·°C
°C

Detailed Energy Balance

Calculated Properties
Total Mass
m₁ + m₂
—
kg
Heat Exchanged
|Q|
—
kJ
Thermal Capacity
Stream A (m₁·Cp₁)
—
kJ / °C
Thermal Capacity
Stream B (m₂·Cp₂)
—
kJ / °C
ΔT — Stream A
|T₁ − Tf|
—
°C
ΔT — Stream B
|T₂ − Tf|
—
°C
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Theory — Conservation of Energy
Adiabatic Mixing Model · Heat Balance Principle

This calculator is based on the Law of Conservation of Energy, which states that energy cannot be created or destroyed — only transferred. When two fluid streams at different temperatures are mixed, the heat lost by the hotter fluid is exactly equal to the heat gained by the cooler fluid (assuming no heat loss to surroundings).

$$Q_{\text{gain}} = Q_{\text{lost}}$$
$$m_1 \cdot C_{p_1} \cdot (T_f - T_1) = m_2 \cdot C_{p_2} \cdot (T_2 - T_f)$$

Solving for the final resultant temperature Tf:

$$T_f = \frac{m_1 C_{p_1} T_1 + m_2 C_{p_2} T_2}{m_1 C_{p_1} + m_2 C_{p_2}}$$
Variable Definitions
\(m_1,\; m_2\)Mass or mass flow rates of each fluid stream (kg or kg/s)
\(C_{p_1},\; C_{p_2}\)Specific heat capacities of the two fluids (kJ/kg·°C)
\(T_1\)Initial temperature of the cold fluid (°C)
\(T_2\)Initial temperature of the hot fluid (°C)
\(T_f\)Resultant / final equilibrium temperature (°C)
\(Q\)Heat transferred between the two streams (kJ)
Application Examples
🧊 Media Supply Unit Load Computation
In processing industries, cold utilities (ice water, propylene glycol, brine) are supplied from an Ice Bank Tank (IBT). Warmer return streams from chillers and pasteurizers are mixed before re-entering the tank. This tool computes the resultant return temperature to ensure it does not exceed the IBT's cooling capacity.
🧪 Batch Preparation
Mixing fluids at different temperatures is fundamental in batch processing. Determining the final equilibrium temperature is critical for: accurate Heat Exchanger Design (LMTD calculations), and maintaining precise temperature control for product quality and process consistency.
🔀 Three-Way Valve Shunting — Closed Loop
When hot or cold water is shunted in a closed loop via a three-way diverting valve, a partial mass flow of media or product is diverted and mixes back into the main loop. This tool computes the resultant temperature of that mixed stream, which is essential for calculating the heat load of the resultant mixture and ensuring the loop stays within design operating limits.
⚠ Assumption — No Heat Loss to Surroundings: This model assumes adiabatic mixing. In large-scale industrial piping, some energy is lost to the environment, though it is typically negligible when pipes are well-insulated.