Heat added to system increases mass

[ChiralSuperfields]

Homework Statement

Please see below

Relevant Equations

Please see below

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!

 

[hutchphd]

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

 

[ChiralSuperfields]

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

Thank you for your reply @hutchphd!

Reference for quote is https://openstax.org/books/universi...4-heat-transfer-specific-heat-and-calorimetry

Many thanks!

 

[gmax137]

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.

 

[ChiralSuperfields]

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.

Thank you for your reply @gmax137!

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

Many thanks!

 

[bdrobin519]

Homework Statement: Please see below
Relevant Equations: Please see below

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.

 

[256bits]

Homework Statement: Please see below
Relevant Equations: Please see below

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

 

[haruspex]

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.

 

[jbriggs444]

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

 

[gmax137]

I don’t think you meant that.

You're right, it was late here when I wrote that.

Q = mCpΔT -->> Equation 1.5 in the book

This ^^
Or, in words:

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

 

[ChiralSuperfields]

Thank you for your help @bdrobin519 , @256bits , @haruspex, @jbriggs444 , and @gmax137 !

 

[malawi_glenn]

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.

 

[jbriggs444]

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".