Physics unit 2 - Thermal physics and Electicity

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john !!
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Thermal Physics:

Equations to know and understand:

∆Q = mc∆T

∆Q = VI∆t
∆Q = F∆x

You can equate any of these (∆Q is energy change):

Say a heater with voltage across it 21 V and current 3 A runs for 200 s to heat up 3 kg of water. The s.h.c. of water is 4200 J Kg^-1 K^-1. The water's initial temperature is 300 K. What is it's new temperature?

Equate: VI∆t = mc∆T
Substitute: 21 x 3 x 200 = 3 x 4200 x ∆T
Rearrange: ∆T = 1 K
New temp = 300 + 1 = 301 K

(LOL... I just plucked completely random numbers from my head! I swear.. then typed them in the calculator... had to check 3 times to make sure I didn't type 12600 in twice... lol that's such a coincedence!!)

Also, the specific latent heat equations is important. This tells you how much energy is needed to melt or boil a substance per unit mass:

∆Q = ml

Where l is the specific latent heat (energy required to melt 1 kg of substance). For example:

500 kJ are used to melt a certain mass of ice. The specific latent heat of fusion of the water is 330 kJ kg^-1. Find the mass of the ice.

Quote equation: ∆Q = ml
Substitute values: 500 000 = 330 000 m
Rearrange to solve: m = 1.52 kg (3 s.f.)

Try these:

1. A 1 kW electric heater is running, in water, and heats 10 kg up by 12 degrees. How long does the heater work for?

2. 32 C passes though an electric heater, powered by a mains plug (240 V). If the water's mass is 700 g, and it's new temperature after the coulombs have passed is 350K, what was the original temperature of the water?

3. Three glases of water, each with a volume of V ml, are at a temperature 80*C. A 50 kΩ resistor, which transferrs all the electrical work done on it to heat, passes 12 kC of charge in two minutes. All the energy from this goes to heating the water. After this time has passed, the water has all evapourated to steam at 112*C. The specific latent heat of vapourisation of water is 2.26 MJ kg^-1, and the specific heat capacity of water and steam is 4.18 kJ kg^-1 K^-1. Find the volume V of one of the glasses. (this one is a long one! I hope I didn't make any mistakes when typing it)

4. A river is modelled as having a semi-circular cross sectional area with it's depth equal to it's radius. The width of the river is 10m, and the average speed of the water is 0.7 m s^-1. A factory decides to use the river as it's cold sink (got some heat engines in there!), and submerges a hot cable that radiates heat to the water at a rate of 2000W. Calculate the temperature difference of the water downstream and the water upstream of the factory.

(I will try these myself).

Heat Engines and Heat Pumps:

A Heat engine, for 3 marks, is something that takes energy from a hot source, uses it to do work, and releases the remainng energy to a cold sink. The efficiency of a heat engine is the useful work done by the engine divided by the total energy transferred from the hot source. The maximum efficiency, of a heat engine is 1 - the temperature of the cold sink divided by the temperature of the hot source. So obviously, if they are further apart the engine will be more efficient.

A heat pump is exactly the opposite - it is given work, and uses this to transfer energy against the natural flow - from a cold sink to a hot source. Like a refrigerator - the power supply in the back, plus the energy taken out of inside it are given to the surroundings - so actually they heat up your room because they require work to cool someone down when it is already colder than it's surroundings.

Pressure

Boyle's Law states that at a constant temperature and with a fixed amount of gas molecules, the pressure exerted on a gas is inversely proportional to the volume of that gas. It helps to think of a bubble rising. Deep down, the water pressure is very high, but as it rises, the pressure falls and the volume of the bubble increases.

The Pressure Law states that with a fixed volume, and with a fixed number of molecules, the pressure that a gas exerts is directly proportional to the temperature of that gas. Obviously this cannot be tested at absoluter zero, but lab results can be extrapolated and they point to this value when the pressure is zero.

There are some equations to learn:

PV/T = k
So P1V1/T1 = P2V2/T2

the constant is reliant on the fact that the same number of moles exists each time. We can say that for a different number of moles,

PV/T = nR, where n is the number of moles and R is the molar gas constant - the pascal metres cubes per kelvin mole... yeah, that doens't make much sense to me either. But the fact it this is a real constant.

We can also write this:

PV = nRT

That's about all I can write at the moment... I'm not too good on gas laws such as the mean square speed, so I'll revise them tonight and perhaps add to this tomorrow. Maybe the same with electricity!

Good luck with those calculations, they are probably way more complicated than you'll get in the exam, but still good practice and a good test to understanding of lots of equations.

mike
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john !!
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Oh, and can someone help me understand the gas law stuff... what does R mean? And what are all the equations? I seem to see a different one everytime I look.
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vp03
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(Original post by mik1a)
Oh, and can someone help me understand the gas law stuff... what does R mean? And what are all the equations? I seem to see a different one everytime I look.
basically you have an equation combinin all the gas laws in

PV/T= constant
the constant depends on the amount of gas used, in moles so u get nR (where n is the number of moles). This R has a value of 8.31 J /mol/K and is called the molar gas constant.

not too clear but the best i can do.
can anyone elaborate on this?
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john !!
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I know that equation, what I didn't understand was the actual meaning of R... in words.. like is it the number of joules needed to heat 1 mole of gas by 1 kelvin?

wait a sec..

PV = nRT
R = PV/nT

so the units are: Pa m^3 mol^-1 K^-1... is Pa m^3 the same as a Joule?
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vp03
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R is just the molar gas constant.

as u know, p proportional to temperature
volume proportional to temperature
so u get PV proportional to T
since it is a proportionality (aint got the sign) to convert it to a equation, u need to stick in a constant which happens to be R (molar gas constant). the reason it is molar is cus it depends on amount of gas.
hence u get
pv/t = r

hope it helps
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john !!
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Yeah that's the part I get, but with some constants you can define in a sentence which would help me understand. eg.

Specific heat capacity of water is the energy required to raise the temperature of 1 kg of water by 1 K
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vp03
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dnt know it that way.

latent heat of fusion is the energy needed for 1 kg of substance to change from solid to liquid. if it is liquid to solid, does it give out this energy?
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john !!
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(Original post by vp03)
dnt know it that way.

latent heat of fusion is the energy needed for 1 kg of substance to change from solid to liquid. if it is liquid to solid, does it give out this energy?
Yes, but that was just an example to illustrate my point about the molar gas constant...
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Economist
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(Original post by mik1a)
Yes, but that was just an example to illustrate my point about the molar gas constant...
Yea it would help understanding if you could define the molar gas constant. The best i can do is it's a number which makes an equation work - like all constants :rolleyes:
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vp03
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yeh i know. i was just confirming the statement cus i was readin on heat engine n didnt understand it.

can anyone explain how a heat engine n pump work?
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john !!
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Heat Engines and Heat Pumps:

A Heat engine, for 3 marks, is something that takes energy from a hot source, uses it to do work, and releases the remainng energy to a cold sink. The efficiency of a heat engine is the useful work done by the engine divided by the total energy transferred from the hot source. The maximum efficiency, of a heat engine is 1 - the temperature of the cold sink divided by the temperature of the hot source. So obviously, if they are further apart the engine will be more efficient.

A heat pump is exactly the opposite - it is given work, and uses this to transfer energy against the natural flow - from a cold sink to a hot source. Like a refrigerator - the power supply in the back, plus the energy taken out of inside it are given to the surroundings - so actually they heat up your room because they require work to cool someone down when it is already colder than it's surroundings.
Like I said above...

Imagine a steam engine. the hot source (steam) is used to do work in pistons (making the train move), and the rest of the energy goes to the cold sink (chimney).
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vp03
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i read it but didnt understand it.


how do u get the boyle's experiment's graph to be linear. It is an exponential graph. so how do u get it into form y=mx +c. i know it has something to do with 1/v or something but dnt know how to get dat. thanks
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crana
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(Original post by vp03)
how do u get the boyle's experiment's graph to be linear. It is an exponential graph. so how do u get it into form y=mx +c. i know it has something to do with 1/v or something but dnt know how to get dat. thanks
Boyle's law is not exponential, it's an example of inverse proportion.

as you know, PV = constant
i.e. P = constant /V

so if you plotted P against V, it's like a y = 1/x curve, not a straight line.

if you plot P against 1/V, then it's like

y = mx + c
P = constant * 1/V + 0

make sense?

rosie
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vp03
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(Original post by crana)
Boyle's law is not exponential, it's an example of inverse proportion.

as you know, PV = constant
i.e. P = constant /V

so if you plotted P against V, it's like a y = 1/x curve, not a straight line.

if you plot P against 1/V, then it's like

y = mx + c
P = constant * 1/V + 0

make sense?

rosie
so the equation will be

P = 1/v

or V = 1/P

and wut about the constant? is dat the molar gas constant?

so its either P=k/v
or V= k/p

is dat rite?
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john !!
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Hmm... I think you may have explained it to me without meaning to!

You can say P (proportional to) 1/V, and so P = k/V. This constant is not quite the molar gas constant, because for this constant to work, T and n must be constant (the temperature and number of moles).

If you combine this with the Pressure law, P/T = k, then you get PV/T = k. This erases the need for a constant temperature, but still you need a fixed amount (moles) of gas, otherwise k will have to vary. So you say R is the value of k for ONE mole of gas. Therefore we split k into nR, where n can vary but R cannot - R is the molar gas constant, and can be multipled by any number of moles (n) to find the temp/pressure/volume conditions for that amount of gas:

PV/T = nR
PV = nRT

Also, from the derivation:

P = p/3 <c^2> (take P as pressure and p as density),

Which comes from:

PV = nm/3 <c^2>
P = nm/3V <c^2>

As n is the number of molecules, and m is the mass of one molecule, nm is the mass of the gas. Divided by V, this gives the density of the gas.

But also, as we know PV = nRT,

PV = nm/3 <c^2>
nRT = nm/3 <c^2>

This can be simplified if we assume on both sides that we are using only one mole. Therefore on the LHS, n becomes 1 (as n on the LHS is the number of MOLES), and on the RHS, n becomes Avagadro's constant (as n on the RHS represents the number of molecules, and Avagadro's constant - N - is the number of molecules in a mole).

RT = Nm/3 <c^2>

This can be rearranged to:

1/2 m<c^2> = 3R/2N T

LHS look familiar? it is the kinetic energy of one mole of gas. Because 3R/2N is a constant (in fact R/N is shortened to just k, where k is the Boltzmann constant), this shows that temperature and kinetic energy of a gas are directly proportional.

That's what 2 hours of work taught me at midnight last night.. :cool:
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crana
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(Original post by vp03)
so the equation will be

P = 1/v

or V = 1/P

and wut about the constant? is dat the molar gas constant?

so its either P=k/v
or V= k/p

is dat rite?
no the equation will not be either P = 1/v

or V = 1/P .

You can *plot* P *against* 1/V to get your straight line graph. It's better to do 1/V instead of 1/P because V is the dependent variable.

the constant is nRT from PV = nRT (I think), but don't worry about that when you are plottingh the graph.

Can you see that if p = nRT/v, if you plot P against 1/V the gradient of the graph will be nRT? (from y = mx + c)

let me know if you want it explaining more

rosie
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vp03
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pls explain cus this just confused me so much more (thanks by da way)
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crana
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(Original post by vp03)
pls explain cus this just confused me so much more (thanks by da way)
well...which bits don't you understand? rosie
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