# Heat added to system increases mass

• member 731016
In summary, according to this, adding heat to a system increases the mass of the particles within it, and the effect of E=mc^2 is negligible.
member 731016
Homework Statement
Relevant Equations
According to this,

The heat added to the system is proportional to the mass. Does someone please know how that highlighted statement is so? I think it is because the heat increases the internal energy of a system and internal energy is the sum of the translational, rotational, and vibrational kinetic energies and also potential energy (I'm not sure what types thought). Therefore, the mass of the system should increase since the particles will have more mechanical energy.

Many thanks!

It is a courtesy to reference the source of the quote. Please do so. "This" is not a reference

member 731016
Your highlighted sentence is just poorly worded, leading to your confusion. It is saying that the change in temperature is proportional to the mass, not that the mass changes.

The effect of E=mc^2 is entirely negligible in these heat transfer calculations.

Lnewqban and member 731016
gmax137 said:
Your highlighted sentence is just poorly worded, leading to your confusion. It is saying that the change in temperature is proportional to the mass, not that the mass changes.

The effect of E=mc^2 is entirely negligible in these heat transfer calculations.

However, how is the change in temperature proportional to the mass?

Many thanks!

ChiralSuperfields said:

According to this,
View attachment 325969
The heat added to the system is proportional to the mass. Does someone please know how that highlighted statement is so? I think it is because the heat increases the internal energy of a system and internal energy is the sum of the translational, rotational, and vibrational kinetic energies and also potential energy (I'm not sure what types thought). Therefore, the mass of the system should increase since the particles will have more mechanical energy.
View attachment 325970

Many thanks!
Material matters as well as atmosphere. Some materials will begin oxidizing or dissolving.

berkeman
ChiralSuperfields said:

According to this,
View attachment 325969
The heat added to the system is proportional to the mass. Does someone please know how that highlighted statement is so? I think it is because the heat increases the internal energy of a system and internal energy is the sum of the translational, rotational, and vibrational kinetic energies and also potential energy (I'm not sure what types thought). Therefore, the mass of the system should increase since the particles will have more mechanical energy.
View attachment 325970

Many thanks!
I think you got off track there.
Q = mCpΔT -->> Equation 1.5 in the book
is the formula that is being discussed

The equation says that the heat added is proportional to the mass and to the change in temperature, with a conversion facture denoted by Cp

gmax137 and DrClaude
gmax137 said:
the change in temperature is proportional to the mass
I don’t think you meant that.

@ChiralSuperfields, It says that the heat injected is proportional to the mass (all else being constant, including the temperature rise) and the heat injected is proportional to the temperature rise (all else being constant, including the mass).
Combining the two, the heat injected is proportional to the product of the temperature rise and the mass.

member 731016 and DrClaude
If you want to warm two bricks, it takes twice as much heat as to warm only one.

member 731016 and Steve4Physics
haruspex said:
I don’t think you meant that.
You're right, it was late here when I wrote that.
256bits said:
Q = mCpΔT -->> Equation 1.5 in the book
This ^^
Or, in words:
jbriggs444 said:
If you want to warm two bricks, it takes twice as much heat as to warm only one.

member 731016
ChiralSuperfields said:
Therefore, the mass of the system should increase

Keep in mind, that the text you quoted also wrote "to a good approximation".

For instance, lets take 1 kilogram of water. Raising its temperature by 1 K requires energy 4182 J.
This is equivalent to, according to ##E=mc^2## the mass ##4.6\cdot 10^{-14}## kg.

member 731016
malawi_glenn said:
Keep in mind, that the text you quoted also wrote "to a good approximation".

For instance, lets take 1 kilogram of water. Raising its temperature by 1 K requires energy 4182 J.
This is equivalent to, according to ##E=mc^2## the mass ##4.6\cdot 10^{-14}## kg.
We could flip it around the other way. If we add enough heat to double the mass, that will increase the temperature by roughly 21 trillion degrees. By which point the the specific heat of the substance may no longer be unchanged "to a good approximation".

member 731016 and malawi_glenn

## 1. How does adding heat to a system increase its mass?

According to Einstein's theory of relativity, energy and mass are interchangeable as described by the equation E=mc². When heat (a form of energy) is added to a system, the system's total energy increases. This increase in energy results in a corresponding increase in mass, although the change is typically very small and not noticeable in everyday situations.

## 2. Can the increase in mass due to added heat be measured?

In practical terms, the increase in mass due to added heat is extremely small and difficult to measure with conventional instruments. This is because the conversion factor c² (the speed of light squared) is a very large number, making the mass increase for any given amount of energy quite minuscule. Specialized equipment and highly controlled conditions are required to measure such small changes.

## 3. Does the increase in mass affect the system's physical properties?

The increase in mass due to the addition of heat is usually so small that it does not significantly affect the system's physical properties. For most practical purposes, this mass change can be considered negligible. However, in theoretical physics and high-precision experiments, even such small changes can be relevant.

## 4. What examples illustrate mass increase due to added heat?

One common example is heating water. When water is heated, its internal energy increases, leading to a corresponding, albeit tiny, increase in mass. Similarly, in nuclear reactions where large amounts of energy are released or absorbed, the changes in mass are more noticeable and can be measured more precisely.

## 5. How does this concept apply to everyday life?

In everyday life, the mass increase due to added heat is so small that it can be ignored for most practical purposes. For instance, when you heat a pot of water on the stove, the increase in mass is imperceptible. However, understanding this concept is crucial in fields like astrophysics, nuclear physics, and high-energy particle physics, where precise calculations of energy and mass are essential.

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