Heat Work Energy

Overview

Engineering reference data for Heat Work Energy 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.

Heat Transfer

$Q = mc\Delta T$

Sensible heat transfer.

Carnot Efficiency

$\eta = 1 - T_C/T_H$

Maximum efficiency between two temperatures.

Variables

Enthalpy and Heat Capacity

Specific enthalpy represents the total energy per unit mass of a substance, accounting for both its internal energy and the energy from applied pressure. It is commonly measured in J/kg or kJ/kg.

Heat capacity defines the total heat energy required to raise the temperature of an entire system by one degree.

Specific Heat Capacity

Specific heat capacity ($c$) is the heat required to raise the temperature of a unit mass of a substance by one degree. Its value depends on whether the heating process occurs at constant pressure ($c_p$) or constant volume ($c_v$).

• For solids and liquids, the volume change with temperature is negligible, so $c_p \approx c_v$.
• Water has a high specific heat capacity ($\approx 4.19 \text{ kJ/kg} \cdot \text{K}$), making it an effective heat transfer fluid.

Unit Conversions for Heat

Key energy unit equivalencies: $1 \text{ cal} = 4.184 \text{ J}$ $1 \text{ J} = 1 \text{ Ws} = 2.78 \times 10^{-4} \text{ Wh} = 2.78 \times 10^{-7} \text{ kWh}$

Heat Transfer and Work Examples

Calculating Heat for Temperature Change

The heat ($Q$) required to change the temperature of a mass is given by: $Q = c_p \cdot m \cdot \Delta T$

Example: Heating 1.0 kg of water from $0^\circ\text{C}$ to $100^\circ\text{C}$: $Q = (4.19 \text{ kJ/kg} \cdot \text{K}) \times (1.0 \text{ kg}) \times (100 \text{ K}) = 419 \text{ kJ}$

Calculating Mechanical Work

Work ($W$) is the product of a force and the distance moved in the direction of the force: $W = F \cdot l$

Example: The work done by a $100 \text{ N}$ force moving an object $50 \text{ m}$: $W = (100 \text{ N}) \times (50 \text{ m}) = 5000 \text{ J}$

Work Against Gravity

The work done in lifting a mass is given by: $W = m \cdot g \cdot h$

Example: Lifting a $100 \text{ kg}$ mass by $10 \text{ m}$: $W = (100 \text{ kg}) \times (9.81 \text{ m/s}^2) \times (10 \text{ m}) = 9810 \text{ J}$

References

• Original Source