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# Watts to Heat Calculator

How to calculate the watts to heat a substance?Specific heat at constant pressure vs. constant volumeExample: Calculating how many watts to heat water during a time intervalFAQs

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.

• 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 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:

$c = \frac{Q}{m \times ΔT}$

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:

$Q = c \times m \times ΔT$

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):

$Ẇ = \frac{Q}{Δt} = \frac{c × m × ΔT}{Δt}$

⚠️ Strictly speaking, power is not heat per unit time but work per unit time (as we explain in our work and power calculator), although the units are the same (watts). Forms of work are electrical and mechanical work. However, the heat from other sources, such as natural gas or oil burning, is not considered work but heat per unit of time.

## Specific heat at constant pressure vs. constant volume

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.

💡 This calculator has $c$ values predefined for some common substances, including the differentiation between $c_\text p$ and $c_\text v$ 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 10 min or 600 sec 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)/600 s = 278.75 W

💡 Check that your substance doesn't undergo a phase change during the temperature change, as it would require additional energy.

FAQs

### 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).

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

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!

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