Energy Transfer Equation

Reference data and engineering information about energy transfer equation for thermodynamics applications.

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Overview

Engineering reference data for Energy Transfer Equation in thermodynamics.

Key Formulas

First Law

$\Delta U = Q - W$

Energy is conserved — heat added minus work done.

Ideal Gas Law

$PV = nRT$

Relates pressure, volume, and temperature of an ideal gas.

Carnot Efficiency

$\eta = 1 - T_C/T_H$

Maximum efficiency between two temperatures.

Variables

Symbol	Description	Unit
$U$	Internal energy	J
$Q$	Heat	J
$W$	Work	J
$P$	Pressure	Pa
$V$	Volume	m³
$T$	Temperature	K

Practical Example: Energy Transfer with Water

Let's calculate the energy required to heat a specific mass of water.

Given:

Mass of water, $m = 2 \text{ kg}$
Initial temperature, $T_1 = 20 \text{ °C}$
Final temperature, $T_2 = 60 \text{ °C}$
Specific heat of water, $c_p = 4.2 \text{ kJ/kg·°C}$

Calculation: The energy transferred $Q$ is calculated using the formula: $Q = m \cdot c_p \cdot \Delta T$ where $\Delta T = T_2 - T_1$ .

$\Delta T = 60\text{°C} - 20\text{°C} = 40\text{°C}$ $Q = 2 \text{ kg} \times 4.2 \text{ kJ/kg·°C} \times 40 \text{ °C} = 336 \text{ kJ}$

To express this energy in kilowatt-hours (kWh), which is a common unit for electrical energy, we use the conversion $1 \text{ kWh} = 3600 \text{ kJ}$ .

$Q = 336 \text{ kJ} \times \frac{1 \text{ kWh}}{3600 \text{ kJ}} \approx 0.093 \text{ kWh}$

This demonstrates that heating 2 kg of water by 40°C requires approximately 0.093 kWh of energy.

The energy $Q$ calculated above represents the amount of thermal energy stored in the water after it has been heated. This stored energy is a form of internal energy, and the water acts as a simple thermal storage medium. The capacity of a system to store energy in this way is directly proportional to the mass of the substance and its specific heat capacity.