Specific Heat Capacity of a body

[andyrk]

How does the amount of heat absorbed by a body depend on the mass of the body and surrounding conditions such as pressure?

 

[NascentOxygen]

This is a very general question. Perhaps begin by examining the definition of Specific Heat Capacity?

 

[andyrk]

When we supply heat to a body, its temperature increases. The amount of heat absorbed depends on the mass of the body, the change in temperature, the material of the body as well as the surrounding conditions such as pressure.

So we write the equation:
Q=msΔθ

But how does the part in bold happen?

 

[Borek]

Where did you got this pressure thing from?

 

[andyrk]

Resnick Halliday

 

[Borek]

Perhaps they are aiming at the fact specific heat capacity is a function of the surrounding conditions - P and T. No idea why specifically pressure is mentioned. Could be it is a matter of context in which this phrase is used. My RH is a Polish translation published 30 years ago, so trying to track it down is likely to be waste of time.

 

[NascentOxygen]

Resnick Halliday

Can you post a photo of that page?

 

[CWatters]

How does the amount of heat absorbed by a body depend on the mass of the body and surrounding conditions such as pressure?

I don't believe there is a simple answer to that.

Heat is essentially a transfer of energy. If you "apply" an amount of energy to a body the amount that is absorbed depends on how it's applied. For example heating water in a pan over a flame is less efficient than immersing an electric heating element in the water. The same amount of applied energy results in a different amount being absorbed. So at the very least more info is needed on the "surrounding conditions".

If we ignore that issue and invent a method of heating an object in such a way that all the applied energy is absorbed then the amount absorbed is independent of mass. If it's all absorbed then it's all absorbed! However the change in temperature that results will depend on the mass and the heat capacity.

There are several versions of "heat capacity". For example the most common is defined "per unit mass", but you can also define it per unit volume (volumetric heat capacity). However the volumetric heat capacity may depend on pressure. Normally it's assumed to be STP. For solids none of this makes much difference under normal circumstances, you can use whichever version of heat capacity you need depending on what units you have for the amount of "stuff". For gasses the volumetic heat capacity may depend on the pressure as that effects the amount of stuff in a given volume. Perhaps that's what this question is all about?

 

[CWatters]

Table of heat capacities here..
http://en.wikipedia.org/wiki/Heat_capacity#Table_of_specific_heat_capacities

"Mass specific heat capacity"
"Constant pressure molar heat capacity"
"Constant volume molar heat capacity"
"Volumetric heat capacity"

Which you use depends on how you plan to define/measure the amount of stuff in the experiment and what parameters might change or stay constant during the experiment. Clearly units in the equation that relates energy to temperature will need to balance.

 

[andyrk]

Okay, leave the pressure dependence, how does the heat absorbed depend on mass of the body? Is there any explanation to it?

 

[Borek]

The most primitive way of explaining: heat is stored in kinetic energy of molecules. Twice more massive body has two times more molecules, so it can store twice the amount of energy.

 

[Andrew Mason]

Okay, leave the pressure dependence, how does the heat absorbed depend on mass of the body? Is there any explanation to it?

It is not clear what you are asking. Are you asking about heat capacity, specific heat capacity or just ability to absorb heat?

Heat capacity of a body relates heat flow into a body to the change in temperature of the body. Specific heat capacity relates the amount of heat flow to the change in temperature per per unit of mass. Molar specific heat capacity relates the amount of heat flow to change in temperature per mole of substance.

Temperature of a body is a measure of the average translational kinetic energy of the molecules of that body in thermal equilibrium.

Heat flow is a measure of the energy that a body acquires in a thermodynamic process by means other than mechanical work.

If a body has fewer molecules than another body but the same mass (because its molecules are more massive) then it will take less energy to increase the average translational kinetic energy of all the molecules in the first body compared to the second. For this reason, it is generally more useful to compare molar specific heats.

If the molecules of a body have more ways of storing kinetic energy (eg rotation, vibration as well as translational energy), it takes more energy to increase just the translational kinetic energy. So heat capacity depends on the degrees of freedom of the molecules of a body.

If you are speaking about heat capacity of a substance that does no mechanical work as it absorbs heat (no change in volume), the specific heat capacity will be lower than that of a body that does mechanical work as it absorbs heat (eg. a gas expanding). This is why molar specific heats of a gas at constant pressure is higher than molar specific heat at constant volume.Perhaps that will help you clarify the question you want to ask.

AM

 

[CWatters]

The basic relationship is...

Δheat energy stored = ΔTemperature * Amount of stuff * Heat capacity

Where Heat Capacity is a "constant" that depends on the material and it's phase. The units for heat capacity and Amount of stuff obviously have to match so the equation balances. If you use the "mass specific heat capacity" then the equation becomes

Δheat energy stored = ΔTemperature * Mass * Specific Heat capacity

Double the mass will store double the heat energy at the same temperature.