# Units in a heat transferred calculation

• smulc
In summary, the conversation is about someone trying to calculate the change in temperature using the equation q=mc∆T, but they are confused about the units in their answer. They receive help and realize that kg and kg-1 cancel out, resulting in just 1.
smulc
I'm trying to do a calculation using: Heat transferred = mass x specific heat capacity x change in temperature
q=mc∆T

But the value I'm trying to calculate is the change in temperature so I've rearranged the equation to ∆T= q/mc

I think the numbers and answer I have are correct, but the units are confusing me. My answer clearly needs to be in °C, the joules on the top and the bottom will cancel out but then on the bottom I'm left with kg multiplied by kg-1.

3.54 J
450 kg x 4.2 x 103 J kg-1 °C-1

As far as I know, these don't cancel each other out so my answer has the wrong units. I don't know if I've done the entire thing wrong if I'm just confusing myself over something silly. I'd appreciate any help at all.

smulc said:
... on the bottom I'm left with kg multiplied by kg-1.
So are you wondering what to do with kg·kg-1?

kg is the same as kg+1, so what you really have is kg+1·kg-1. Simplify that using algebra rules for exponents, and you should be all set.

ohh I feel really stupid now. Any number to the zero power is equal to 1. I already knew this but mistakingly thought that the result of calculating kg0 would be 1kg, but the answer is literally just 1, isn't it? So the kg does actually cancel. I feel silly for not realising, thanks very much for the help!

You're welcome, glad it worked out for you.

Hello,

Thank you for sharing your calculations and concerns. It seems like you have a good understanding of the equation for heat transferred (q=mc∆T) and how to rearrange it to solve for the change in temperature (∆T= q/mc). However, you are correct that the units for your final answer do not match the desired units of °C.

To solve this issue, you will need to pay attention to the units as you rearrange the equation. Let's break down the units for each term in the equation:

- q (heat transferred) has units of joules (J)
- m (mass) has units of kilograms (kg)
- c (specific heat capacity) has units of joules per kilogram per degree Celsius (J/kg°C)
- ∆T (change in temperature) has units of degrees Celsius (°C)

When you rearrange the equation to solve for ∆T, you will need to make sure that the units on the top and bottom of the equation cancel out, leaving you with only the desired units for ∆T. Let's see how this works:

∆T = q/mc

- q has units of J and is on the top of the equation. On the bottom, we have m (kg) multiplied by c (J/kg°C). This means that the units on the bottom will cancel out, leaving us with only J on the top.
- Since we want our final answer to be in °C, we need to make sure that the units on the top are also in °C. To do this, we can use the specific heat capacity (c) to convert the units of J to °C. Remember, c has units of J/kg°C, which means that it tells us how many joules are needed to raise the temperature of 1 kg of a substance by 1 °C. So, we can divide our answer in J by c to get the units in °C.
- This gives us the final equation: ∆T = q/c. The units for q (J) cancel out with the units for c (J/kg°C), leaving us with only the desired units of °C for ∆T.

Applying this to your specific example:

∆T = 3.54 J / (450 kg x 4.2 x 10^3 J/kg°C)

The units for J cancel out, leaving us with only

## 1. What are the common units used in a heat transfer calculation?

The most commonly used units in a heat transfer calculation are Joules (J), Calories (cal), and British Thermal Units (BTU). These units measure the amount of heat transferred in a system.

## 2. How do I convert between different units in a heat transfer calculation?

To convert between different units in a heat transfer calculation, you can use conversion factors. For example, 1 calorie is equivalent to 4.184 joules, and 1 BTU is equivalent to 1,055.06 joules. You can also use online unit conversion calculators for more complex conversions.

## 3. Can I mix and match units in a heat transfer calculation?

No, it is important to use consistent units in a heat transfer calculation. Mixing and matching units can lead to errors and inaccurate results. Make sure to convert all units to the same system before performing any calculations.

## 4. How do I account for units in my heat transfer equations?

When writing out heat transfer equations, it is important to include the units for each variable. This helps to ensure that all units are consistent and that the equation is balanced. It also allows for easier unit cancellation when solving the equation.

## 5. Are there any specialized units used in heat transfer calculations?

Yes, there are some specialized units that are used in specific heat transfer calculations. For example, in radiative heat transfer, the units of radiative flux density are Watts per square meter (W/m²). In convective heat transfer, the units of heat transfer coefficient are Watts per square meter Kelvin (W/m²K).

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