Deriving general specific heat capacity formula

In summary: That is very interesting what you mention. Sorry I did quite get the bit I put it italic above. I don't understand the bit about hand waving. Is it still correct what the textbook did?
  • #1
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Homework Statement
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Relevant Equations
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For this,
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Dose anybody please know of a better way to derive the formula without having ##c = \frac{\Delta Q}{m \Delta T}## then taking the limit of both sides at ##\Delta T## approaches zero? I thought ##\Delta Q## like ##\Delta W## was not physically meaningful since by definition ##Q## is the heat transfer.

Many thanks!
 
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  • #2
ChiralSuperfields said:
I thought ##\Delta Q## like ##\Delta W## was not physically meaningful since by definition ##Q## is the heat transfer.
Do you think that ##Q## is physically meaningful?
 
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  • #3
kuruman said:
Do you think that ##Q## is physically meaningful?
Thank you for your reply @kuruman!

Yes I do, since it is the quantity of heat transferred.

Many thanks!
 
  • #4
ChiralSuperfields said:
Thank you for your reply @kuruman!

Yes I do, since it is the quantity of heat transferred.

Many thanks!
Well, ##Q##, which is physically meaningful, is not transferred instantaneously all at once but in increments ##\Delta Q##. Why is ##Q## meaningful but not an element ##\Delta Q## that is part of it? BTW, the same reasoning applies to ##\Delta W.##
 
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  • #5
kuruman said:
Well, ##Q##, which is physically meaningful, is not transferred instantaneously all at once but in increments ##\Delta Q##. Why is ##Q## meaningful but not an element ##\Delta Q## that is part of it? BTW, the same reasoning applies to ##\Delta W.##
Thank you for your reply @kuruman!

So could we think of the heat transferred as the summation of the differential heat elements ##dQ## which I think leads to ##Q = \int dQ##.

However, back to the algebra way of thinking, is the reason why the heat element ##\Delta Q## is not meaningful because it is causes a differential change in the state of the system that can be considered negligible?

Many thanks!
 
  • #6
ChiralSuperfields said:
Thank you for your reply @kuruman!

So could we think of the heat transferred as the summation of the differential heat elements ##dQ## which I think leads to ##Q = \int dQ##.

However, back to the algebra way of thinking, is the reason why the heat element ##\Delta Q## is not meaningful because it is causes a differential change in the state of the system that can be considered negligible?

Many thanks!
Why do you insist ##\Delta Q## is not meaningful? In post #3 you agreed that it is.
 
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  • #7
kuruman said:
Why do you insist ##\Delta Q## is not meaningful? In post #3 you agreed that it is.
Thank you for your reply @kuruman!

Yeah I guess it is meaningful if we think of it has a differential heat element not as ##Q_f - Q_i## which cannot be true since heat is state variable.

Many thanks!
 
  • #8
The specific heats are defined in terms of derivatives of intenal energy or entropy not of heat. And as definitions, they cannot be proven.
The heat is not a function of state so using the derivative of heat in respect to temperature it may be a little hand waving.
 
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  • #9
nasu said:
The specific heats are defined in terms of derivatives of intenal energy or entropy not of heat. And as definitions, they cannot be proven.
The heat is not a function of state so using the derivative of heat in respect to temperature it may be a little hand waving.
Thank you for your reply @nasu!

That is very interesting what you mention. Sorry I did quite get the bit I put it italic above. I don't understand the bit about hand waving. Is it still correct what the textbook did?

Many thanks!
 

FAQ: Deriving general specific heat capacity formula

What is specific heat capacity?

Specific heat capacity is the amount of heat required to raise the temperature of one gram of a substance by one degree Celsius (or one Kelvin). It is a property that varies with different materials and is typically denoted by the symbol \( c \).

Why is deriving the general specific heat capacity formula important?

Deriving the general specific heat capacity formula is important because it provides a fundamental understanding of how different materials absorb and transfer heat. This knowledge is crucial in fields such as thermodynamics, material science, and engineering, where precise temperature control and energy management are essential.

What is the general formula for specific heat capacity?

The general formula for specific heat capacity is given by \( c = \frac{q}{m \Delta T} \), where \( q \) is the amount of heat added, \( m \) is the mass of the substance, and \( \Delta T \) is the change in temperature. This formula helps to quantify the heat capacity of a material based on empirical measurements.

How do you experimentally determine the specific heat capacity of a substance?

To experimentally determine the specific heat capacity of a substance, you can use a calorimeter. By measuring the amount of heat added to a known mass of the substance and the resulting temperature change, you can apply the formula \( c = \frac{q}{m \Delta T} \) to calculate its specific heat capacity. Ensuring accurate measurements of heat, mass, and temperature change is crucial for reliable results.

What factors can affect the specific heat capacity of a material?

The specific heat capacity of a material can be affected by several factors, including its physical state (solid, liquid, or gas), temperature, and pressure. Additionally, the molecular structure and bonding of the material play significant roles in determining how much heat energy is required to change its temperature.

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