# A question about the specific heat and Debye temperature

• patric44
In summary: C.In summary, the conversation discussed the relationship between temperature scales and heat capacity. It was concluded that the conversion between K and °C is only applicable for temperature values, not intervals, and that heat capacity remains the same regardless of the temperature scale used. The use of absolute temperatures is necessary in equations involving temperature.
patric44
Homework Statement
it was a problem written in a book , asking to calculate the specific heat of a substance given the specific heat of another one and their Debye temperatures
Relevant Equations
C = constant/Θ^3

this is my attempt of a solution , but my only equation is should i convert Θ to Celsius , and if i did the specific heat of the other
substance is greater , how is that if its inversely proportional with temperature ! . and the other Θ is 200 K so it should be less ?!

The heat capacity is defined as the amount of heat to be supplied to a given mass of a material to produce a unit change in its temperature. The unit change in temperature (whether given in ##K## or ##°C##) is the same as they differ only by some constant (here ##273.15 K##).

Lord Jestocost said:
The heat capacity is defined as the amount of heat to be supplied to a given mass of a material to produce a unit change in its temperature. The unit change in temperature (whether given in ##K## or ##°C##) is the same as they differ only by some constant (here ##273.15 K##).
so which one is correct the first solution or the second , the fact is that constant is not a multiplying factor ,rather subtraction (T-273) suggest that it will not cancel between the numerator and denominator .
so the ration is not the same .
which one is correct ? and if it was the second one ,why? since CB is larger ! although its inversely proportional with Debye temperature .

You should not convert Θ to Celsius. Your equation assumes absolute temperatures. You are correct that having a different zero on the temperature scale means the ratio will come out differently.

mjc123 said:
You should not convert Θ to Celsius, and if you do, you don't do it by subtracting 273!
so my first answer was correct .
how should i convert it ?

Sorry, made a mistake there - I've corrected it. Why do you want to convert your answer? To what?
Do you mean you want to convert J/kgK to J/kg°C? How do you think you would do that?
Do you appreciate the difference between converting a temperature value in K to °C (or vice versa), and converting a temperature interval in K to °C?

mjc123 said:
Sorry, made a mistake there - I've corrected it. Why do you want to convert your answer? To what?
Do you mean you want to convert J/kgK to J/kg°C? How do you think you would do that?
Do you appreciate the difference between converting a temperature value in K to °C (or vice versa), and converting a temperature interval in K to °C?
i want to convert it because the fact the the specific heat was given with J/kg°C seemed a little tricky after seeing Θ in K , i thought there must be a trick or something . and since the conversion factor is not a multiplication suggests that i should or the ratio will be different.
Isn't the conversion between k to c is just T-273. I don't understand your last question

The °C and K temperature scales have the same scale factor but a different zero. As T(K) = T(°C) + 273, if you increase T from 283 to 293 K, you increase it from 10°C to 20°C. The increase is 10 degrees in each case, because the scale factor is the same. If you are converting a temperature value (a point on the scale) from K to °C, you subtract 273. If you are converting a temperature difference in K to one in °C, the number is the same.

When you are considering heat capacity, you are considering the heat needed to change the temperature by a given amount. This temperature difference is the same in K or °C, so the heat capacity has the same value in J/kgK or J/kg°C. However, that does not mean that you can use temperature values in K or °C as you choose in the equation. The equation requires absolute temperatures, i.e. in a scale where the zero of the scale comes at absolute zero.

To give another example, T(°F) = 1.8*T(°C) + 32. Here there is both a zero offset and a different scale factor (1.8). This means a temperature difference of 10°C will be the same as a difference of 18°F. You often see in the news statements by reporters who know, e.g., that 10°C = 50°F, and will talk of a temperature of "-10°C (-50°F)" or "the temperature increased by 10°C (50°F)". Can you see why these are wrong?

Oh you mean that the specific heat is just concerned with the change in temperature which is T2-T1 and the 273 will cancel so its the same as the difference between Celsius.
am I correct

I'm not sure what you mean by that, as T1 = T2 in your picture, but the point is that an interval of 1K is the same as an interval of 1°C. But T and Θ in your equation must both be in K, because the 273 doesn't cancel when you divide.

I meant an interval by "T2-T1".
Just to be sure here 1.14*10^-3 is the correct answer
Thanks so much for helping

## 1. What is specific heat and why is it important?

Specific heat is the amount of energy required to raise the temperature of a substance by 1 degree Celsius. It is an important property because it helps determine how much energy is needed to heat or cool a substance, and it can also provide information about the molecular structure and composition of a material.

## 2. How is specific heat measured?

Specific heat is typically measured using calorimetry, which involves measuring the temperature change of a substance when a known amount of heat is added or removed. The specific heat is then calculated using the formula Q = mcΔT, where Q is the amount of heat added, m is the mass of the substance, c is the specific heat, and ΔT is the change in temperature.

## 3. What is the relationship between specific heat and Debye temperature?

The Debye temperature is a characteristic temperature of a material that describes the average energy of its atoms or molecules. It is related to specific heat because as the Debye temperature increases, the specific heat of a material also increases. This is due to the fact that higher Debye temperatures indicate a more complex molecular structure, which requires more energy to change the temperature of the substance.

## 4. How is specific heat related to the thermal conductivity of a material?

The thermal conductivity of a material is a measure of how well it conducts heat. Specific heat and thermal conductivity are related because materials with higher specific heat also tend to have higher thermal conductivity. This is because materials with more complex molecular structures are better able to transfer heat energy between particles.

## 5. Can specific heat and Debye temperature be used to identify unknown substances?

Yes, specific heat and Debye temperature can be used as identifying properties for substances. By measuring these properties and comparing them to known values, scientists can determine the molecular structure and composition of a substance, helping to identify it. However, other factors such as density and melting point should also be considered in identification processes.

• Introductory Physics Homework Help
Replies
15
Views
931
• Introductory Physics Homework Help
Replies
2
Views
880
• Introductory Physics Homework Help
Replies
1
Views
1K
• Introductory Physics Homework Help
Replies
12
Views
552
• Introductory Physics Homework Help
Replies
3
Views
1K
• Introductory Physics Homework Help
Replies
3
Views
969
• Introductory Physics Homework Help
Replies
2
Views
311
• Introductory Physics Homework Help
Replies
2
Views
253
• Introductory Physics Homework Help
Replies
3
Views
892
• Introductory Physics Homework Help
Replies
21
Views
2K