## Wattage Required to Heat Liquids and Gases

P = | m • c • ΔT | • SF |

t |

Where:

P = Power (kW)

m = Mass (kg)

If, instead of mass, the known variable is total volume, use the following equation:

m = V • p |

Where:

V = Volume (m^{3})

p = Density (kg/m^{3})

If, instead of mass or volume, the known variable is a flow rate, before using the above equation we must determine the equivalent volume that would be filled in one second at this flow using the following equation:

V = | V̇ | • 0.001 (m^{3}/L) • 1 (second) |

60 (seconds/minute) |

Where:

V = Volume (m^{3})

V̇ = Volumetric Flow Rate (L/min)

If the volume provided/calculated is at operating pressure and temperature, we need to determine the equivalent volume at ambient temperature and pressure (ATP) using the equation below:

V_{ATP} = V_{O} • |
T_{ATP} |
• | P_{O} |

T_{O} |
P_{ATP} |

Where:

V_{ATP} = Volume (m^{3}) at STP

V_{O} = Volume (m^{3}) at Operating Conditions

T_{ATP} = Standard Temperature (°K) ≈ Typically 298.15°K

T_{O} = Operating Temperature (°K)

P_{ATP} = Standard Pressure (kPa) ≈ Typically 101.325 kPa

P_{O} = Operating Pressure (kPa)

NOTE: ATP can vary depending on the environment and application

NOTE: The above formula has been derived from the Ideal Gas Law, and therefore only applies to fluids which behave as ideal gases.

c = Specific Heat Capacity (kJ/kg•K)

Specific Heat Capacity is a material specific property. It is the amount of thermal energy required to raise the temperature of the material per unit of mass. If different materials are being heated in the system, then the power equation above will have to be redone for each individual material.

ΔT = Change/Difference in Temperature (°K)

If the temperature is provided in degrees Celsius, the units do not need to be converted because we are using the change in temperature.

t = Time (sec)

SF = Safety Factor

A safety factor will be necessary because there are losses and inefficiencies in every system. The safety factor required is dependent upon the expected efficiency of application/system being analyzed. If no safety factor is included, the calculated power is a theoretical value that assumes 100% perfectly efficient heat transfer.