Thermal energy is present everywhere, and calculating the watts to heat a substance is essential to know how much resources we'll spend.

We use heat for cooking our food, keeping us warm, drying different objects, and more. For that reason, it's so relevant in our lives.

Read on to learn more about:

  • How to calculate the watts to heat any substance.
  • How to use this calculator.
  • How much to run a 1500 watt heater (cost per hour, day, or month).

How to calculate the watts to heat a substance?

Before digging into how to calculate the watts to heat something, let's look at the specific heat formula. Specific heat (aka specific heat capacity) is the property of a material that specifies the amount of energy needed to increase its temperature in one unit per unit mass. This formula defines it:

c=Qm×ΔTc = \frac{Q}{m \times ΔT}

where:

  • c – Specific heat;
  • Q – Energy added (usually in the form of heat) to increase the temperature;
  • ΔT – Temperature change; and
  • m – Mass of the object.

If you know the heat capacity and mass of some material, you can predict the energy needed to cause any temperature change to it:

Q=c×m×ΔTQ = c \times m \times ΔT

If we divide both sides of the equation by time, we get the power necessary () to cause a specific temperature change during a certain time interval (Δt):

W˙=QΔt=c×m×ΔTΔtẆ = \frac{Q}{Δt} = \frac{c × m × ΔT}{Δt}

Specific heat at constant pressure (cₚ) vs. constant volume (cᵥ).

Causing a temperature change can require different amounts of heat, depending on how we execute the process. Suppose we do it at constant pressure and, therefore, the substance is allowed to expand as we transfer the heat. In that case, we require more heat than if it were at constant volume. That occurs because, at constant pressure, we need additional energy to cause the expansion.

For that reason, in thermodynamics, we define two kinds of specific heats: 1. specific heat at constant pressure (cₚ), and 2. specific heat at constant volume (cᵥ).

As they are considered almost incompressible, and their volume doesn't significantly change, for liquids and solids, cₚ and cᵥ are equal (cₚ = cᵥ). But for gases, it's essential to make the differentiation.

💡 This calculator has c values predefined for some common substances, including the differentiation between cₚ and cᵥ for gases.

Example: Calculating how many watts to heat water during a time interval

Suppose you're interested in how many watts are needed to heat 1 kg of water and increase its temperature by ΔT = 40°C = 40 K. The time to accomplish this task is 10 min, and you found on the internet that the specific heat of the water is 4181.3 J/kg·K. To know the required watts to heat that amount of water, follow these steps:

  1. Input 40 °C or 40 K in the "Change of temperature (ΔT)" box.
  2. Input 1 kg in the "Mass (m)" box.
  3. Select a custom substance and type 4181.3 J/kg·K in the "Specific heat capacity (c)" box.
  4. Input 1 min or 600 s the "Time to heat (t)" box.
  5. That's it. The required watts to heat the water in that time should be 278.75.

You can check the results with the formula:

Ẇ = Q/Δt = (4181.3 J/kg·K × 1kg × 40K)/600s = 278.75 W

💡 You can click on the advanced mode of the calculator to define the temperature change based on an initial and final temperature. But be careful, check that your substance doesn't go through a phase change during this temperature change, as it would require additional energy.

FAQ

What is the difference between work and power?

The difference between work and power is:

  • Work means energy transfer associated with a force acting through a distance.
  • Power is how fast work is applied.

Examples are:

  • If we exert a force to raise an object, we're applying work to increase its potential energy. The faster we lift it, the higher the power.
  • If an electromotive force moves electrons in a wire, that's an example of electrical work. A more rapid electron transport implies a higher electric power.

How to calculate the cost of an electric heater?

To calculate an electric heater cost, follow these steps:

  1. Determine your heater's power consumption (i.e., 1.5 kW).
  2. Figure out your local electricity cost (i.e., $0.1563 per kW⋅h).
  3. Multiply the power consumption by the electricity cost, and you'll get the hourly consumption (i.e., 1.5 kW × $0.1563/kW⋅h = $0.23445 per hour.).
  • To calculate the daily cost, multiply the hourly cost by the number of hours you use the heater a day.
  • For the monthly cost, multiply the daily cost by the number of days you use the heater a month.

How much does a 1500 watt heater cost to run?

The cost to run a 1500 watt heater per hour is $0.1563, which equals $3.7512 per day and $113 per month for a 24h usage. This answer assumes an average electricity cost of 10.42 cents per kW⋅h.

How to calculate heat from watts?

To calculate heat (actually, temperature change) from watts applied to a substance, use the formula: ΔT = (Δt × Ẇ)/(c × m), where:

  • ΔT – Temperature change experienced by the substance;
  • Δt – Time during which we apply the heat.
  • – Power in Watts with which we heat the substance.
  • c – Specific heat of the substance; and
  • m – Mass.
Luis Fernando
Change of temperature (ΔT)
°F
Mass (m)
lb
Substance (optional)
Custom ▾
Specific heat capacity (c)
J/(kg·K)
Time to heat (t)
sec
Power (Ẇ)
W
A negative power means that we're lowering the temperature of the substance 🥶. We're not providing heat to that substance, but it's transferring heat 🔥 to our environment (heat loss).

This tool calculates the power needed to heat a substance in a specific amount of time. If you're searching for the energy to heat something, independently of the time, you can check our sensible heat calculator.

We made a video that explains thermodynamics concepts on the example of cooling drinks! Watch it here:

Science of cooling drinks

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