Watts to Heat Calculator

Thermal energy is 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)?

Before digging into how to calculate the watts to heat something, let's remember what we saw in the specific heat calculator and look at the heat capacity 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:

where:

• $c$ – Specific heat;
• $Q$ – Energy added (usually in the form of heat) to increase the temperature;
• $\Delta T$ – 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:

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

Causing a temperature change can require different amounts of heat, depending on how we execute the process. Suppose we do it at constant pressure; 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 heat: 1. specific heat at constant pressure ($c_\text p$) and 2. specific heat at constant volume ($c_\text v$).

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

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 10 min or 600 s in 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

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.

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.

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.

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;
• Ẇ – Power in Watts with which we heat the substance;
• c – Specific heat of the substance; and
• m – Mass.