# Watts to Heat Calculator

Created by Luis Hoyos
Last updated: Aug 30, 2022

Thermal energy is everywhere, and calculating the watts to heat a substance can help predict how much power a temperature change will take us.

This watts to heat calculator determines the power required to cause a temperature change in a substance, as long as you specify the temperature change (ΔT), mass (m), its specific heat (c), and time to heat (t).

If you're interested in knowing how this calculator works, in the following sections, we present the power to temperature equation that relates watts to the temperature change in a substance.

## Watts to temperature relationship

The relationship between power and temperature arises from the specific heat capacity, which relates the temperature change in a substance to the heat needed to achieve it:

$\footnotesize Q = c \times m \times ΔT$

, where:

• $Q$ — Heat required to cause the temperature change, in Joules (J);
• $m$ — Mass of the substance, in kilograms (kg);
• $ΔT$ — Temperature change, in kelvin (K) or °C; and
• $c$ — Specific heat of the substance, in J/(kg K);

Dividing both sides of the equation by time, we obtain a formula to calculate the power needed to cause a temperature change in a substance in an amount of time:

$\footnotesize \dot W = \frac{Q}{Δt} = \frac{c × m × ΔT}{Δt}$
• $\Delta T$ — Amount of time, in seconds (s); and
• $\dot W$ — Power, in watts (W); and

🙋 Strictly speaking, power is not heat per unit time but work per unit time (as we explain in our work and power calculator). If the heat comes from an electrical device (i.e., a heater), there's no problem with using the term, as electricity is a form of work. However, the heat we obtain from other sources, such as natural gas or coal burning, is not considered work but heat per unit of time. In either case, the units are the same (watts).

Now that we obtained the power-to-temperature equation, let's take a moment to differentiate between the two types of specific heat.

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

The amount of heat required to cause a temperature change will vary depending on the conditions of the process. For that reason, we define two kinds of specific heat: 1. specific heat at constant pressure (cₚ), and 2. specific heat at constant volume (cᵥ).

At constant pressure, as the substance is allowed to expand, we require more heat than if it were at a constant volume. That's because we need additional energy to cause the expansion.

For solids and liquids, cₚ and cᵥ are the same (cₚ = cᵥ = c), as their volume doesn't significantly change. However, for gases, we need to clarify if the process is at constant pressure or volume.

## How to use this watts to heat calculator

To use this watts to heat calculator, follow these steps:

1. Input the temperature change. For example, if the substance goes from 20 to 40°C, input ΔT = 20°C or ΔT = 20 K.
2. Input the mass of the substance. Let's say it's m = 4 kg.
3. Select the time to heat. Suppose you want to heat those 4 kilograms of substance in t = 3 min = 180 sec.
4. Input the substance. For example, let's say it's liquid water, whose specific heat is c = 4181.3 J/(kg K).
5. That's it! The answer should be 1858.4 watts. You can verify the result with the power to temperature equation of the previous section:
$\footnotesize \dot W = \frac{Q}{Δt} = \frac{c × m × ΔT}{Δt} \\\ \\\ \ \ \ \ \ = \frac{4181.3 \text{ J/(kg K)} × 4 \text{ kg} × 20 \text{ K}}{180 \text{ s}} \\\ \\\ \dot W = \frac{334504 \text{ J}}{180 \text{ s}} = 1858.4 \text{ W}$
Luis Hoyos
Change of temperature (ΔT)
°F
Mass (m)
lb
Time to heat (t)
sec
Substance (optional)
Custom ▾
Specific heat capacity (c)
J/(kg·K)
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).
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