Specific Heat calculations

[ThermalDude]

I see people caculating heat Quantity transferred as Q=Mass * Cp * delta T. All is good with this. But...
But they use weight in lieu of mass when they calculate.
In imperial units Cp of water is 1 BTU/lb-F. Isn't tis really lbm (pounds mass)? They really do as follows:
Q = lbf * 1 BTU/lbm-f * delta T.
(where "lbf" is lb force or weight)
Shouldn't the weight of the water be divided by 32.2 to get lbm?

Is this actually correct:
Q = lbf/32.2 * 1 BTU/lbm-F * Delta T ?

 

[desertfox]

Hi ThermalDude

Yes it should be mass not weight I agree with you, we use metric units here but the equation above we would kg's for mass but weight would be kg's*g.

desertfox

 

[25362]

Desertfox is right. Weight is the name for a force W exerted by Earth on the mass m of a body and is equal to W = mg.

With my 75-kg mass near Earth's surface, my weight is (75 kg)(9.8 m/s[sup]2[/sup]) or 735 N. (N=Newton).
On the moon, where acceleration of gravity is only 1.6 m/s[sup]2[/sup], I would weigh only 120 N.

 

[MintJulep]

Lbf/g is not Lbm

Lbf/g gives you slugs, which is the proper unit of mass in our lovely system.

Is this actually correct:
Q = lbf/32.2 * 1 BTU/lbm-F * Delta T ?

No.

 

[ThermalDude]

Are Slugs and pounds-mass not synonymous? I believe they are.
What is wrong with the equation as written using the Cp of water and assuming we are on earth?
(I need to keep it in the imperial unit system.)

Q = lbf/32.2 * 1 BTU/lbm-F * Delta T

I think this is correct.

 

[ThermalDude]

Upon further thinking, I suspect what is really wrong with this equation is the value used for Cp. Cp SHOULD have units of BTUs/LBm-F, but really when we say Cp of water is 1 BTU/lb-F, we really mean 1 BTU per pound force per degree F. Do you think this is true?

 

[MintJulep]

Are Slugs and pounds-mass not synonymous?

No.

F=ma

1 slug under the influence of Earth's gravity (32.2 ft/s/s) has a weight of 32.2 pounds (force)

A pound (mass) is the mass of an object that has a weight of 1 pound (force). So 1 pound (mass) = 1/32.2 slug

When we say the Cp of water is 1 BTU/lb-F we mean an amount of water that weights a pound on Earth.

 

[IRstuff]

Just to make that perfectly clear, that would be the lb that's equal to 0.4536 kg

TTFN

FAQ731-376

 

[GregoireMC]

The Cp is in Btu/lbm*°F in imperial and in J/g*K
Q= Mass * Cp * delta T
Dimensions:
[BTU] = [Lbm] * [Btu/(lbm*°F)]* [°F]

[Lb m] is a mass (equivalent to grams; given by a scale)
[Lb f] is a force (equivalent to Newtons; Weight= Mass* Gravitity constant)
[Lbf] = [Lbm]*32.174 ft/s^2

[Troll] Use SI and convert in US units after [\Troll]

good online converter (also goo to check the units):

http://online.unitconverterpro.com/

 

[MintJulep]

[Lb m] is a mass (equivalent to grams; given by a scale)

Scales measure force, not mass.

 

[25362]

Adding to MintJulep's last sentence: ...however, since mass and weight are "proportional" in a given location, scales are calibrated to measure mass.

Although a scale measures force, being calibrated in mass units, under the assumption that g = 9.8 m/s[sup]2[/sup], it whould read more if the weighing is done on an upward accelerating elevator.

 

[Compositepro]

Scales that operate on the balance principle (using a counterweight, rather rather than spring force) do indeed measure mass.

 

[25362]

Even balance-type scales (not only spring scales) compare "weights" labelled in mass units.

 

[Compositepro]

A balance will read the same on the earth or or the moon so it is not measuring weight.

 

[SomptingGuy]

While the Kilogram remains defined by an artefact (the IPK), measurement of mass by comparison with the IPK (or copies of it) will invariably involve a balance.


- Steve

 

[25362]

The British unit of force is the pound-force, 1 lbf [≈] 4.45 N
The British unit of mass is the slug; 1 slug [≈] 14.6 kg.

A supermarket hanging spring scale measures the object's weight, but since mass and weight are proportional at a given location, it also provides a measure of the object's mass.

 

[GregoireMC]

I meant the result given by a scale, not what it actually "measure".

I think scales with springs are measuring forces (weight), balances are giving the equilibrium between two torques (force x distance), and piezo-electrics scale are measuring a pressure (force / surface)... Isn't it?

In all case the display is giving the mass.

 

[vpl]

Thermaldude

Getting back to your original question.

The formula is actually Q=[ṁ]c[sub]p[/sub][Δ]T.

The little dot over the m means that it is a mass flow rate -- not just a mass. For working in English system, I use pounds-mass/hour. Yes you have to make sure that you are using pounds mass and not pounds force.




Patricia Lougheed

******

Please see FAQ731-376: Eng-Tips.com Forum Policies for tips on how to make the best use of the Eng-Tips Forums.

 

[MintJulep]

If you put a dot of the m you need to put a dot over the Q too.

Without dots over either the equation is perfectly suitable to figure how much heat was added to a fixed mass to raise the temperature by dT.