What Are the Key Steps to Solve A-Lev Physics Gas and Thermal Exam Questions?

[NeroBlade]

Hey folks I been going through past exam papers and got 4 questions which are hard to follow, for those that know please provide a detailed step by step guide. I have completed most of the previous parts of each question which got me some extra values.

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Question 1

OK here's what I have worked out so far:

Volume = 5*10^-3
Mass = 8*10^-3
Pressure = 900000
n = 2
molecular mass = 4
r.m.s Speed of all molecules = 1300

Question asks the r.m.s speed of all molecules when the Kelvin temperature has doubled. All I know is that speed is proportional to temperature.

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Question 2

Should be quick and simple

Use an ideal gas equation and kinetic theory formula pV = (1/3)Nmc^2 to show the equivalent formula is U = N * (1/2)mc^2

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Question 3

Pressure = 1.5*10^16
Density = 1.8*10^5
r.m.s Speed = 500000
Number of protons per m^3 = density/proton mass = 1.08*10^32

Question asks me to calculate the number of moles per m^3 and then the temperature.

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Question 4

Concerning a water radiator

Metal sheet dimensions = 0.9*1.5*0.005m
Solar Radiation arrives at 350W
Water pumped at (0.45/60)W
Temp' Difference = 26 - 15 degs = 11 degs
Mass of water = 1kg
Heat Capacity = 4200

Calculate the percentage of solar energy transferred to water.

Then, using the formula Q/t = -kA(temp diff/x)
Make a rough estimate of the temperature difference between top surface and bottom of aluminium sheet.

Any help would be great!

 

[Redbelly98]

I see that nobody has responded in almost 2 days. Actually there are reasons for this. For one, it's better to post each question as separate threads. Individuals may be able to help you with 1 or 2 questions, but are less inclined to respond when they see all these questions in one thread.

Hey folks I been going through past exam papers and got 4 questions which are hard to follow, for those that know please provide a detailed step by step guide. I have completed most of the previous parts of each question which got me some extra values.

=======
Question 1

OK here's what I have worked out so far:

Volume = 5*10^-3
Mass = 8*10^-3
Pressure = 900000
n = 2
molecular mass = 4
r.m.s Speed of all molecules = 1300

Question asks the r.m.s speed of all molecules when the Kelvin temperature has doubled. All I know is that speed is proportional to temperature.

Not true. However, Kinetic energy is proportional to temperature. That fact, and the relation between speed and kinetic energy, will help here.

Question 2

Should be quick and simple

Use an ideal gas equation and kinetic theory formula pV = (1/3)Nmc^2 to show the equivalent formula is U = N * (1/2)mc^2

According to our forum rules, you'll need to show an attempt at solving this, or at least give your thoughts on how to start solving it, before getting help. This is another reason why nobody has replied until now.

(You took a starting stab at Question 1, so I responded with a hint for that one.)

Question 3

Pressure = 1.5*10^16
Density = 1.8*10^5
r.m.s Speed = 500000
Number of protons per m^3 = density/proton mass = 1.08*10^32

Question asks me to calculate the number of moles per m^3 and then the temperature.

Again, show your thoughts on what might be done to solve this. Also: UNITS UNITS UNITS. There are many different pressure units used for these problems: atm, mm Hg, and N/m² to name the more common ones. Is that density in moles/cm³? kg/m³? Other?

Question 4

Concerning a water radiator

Metal sheet dimensions = 0.9*1.5*0.005m
Solar Radiation arrives at 350W
Water pumped at (0.45/60)W

What does that mean? I've never heard of water pump rates expressed in Watts. It's usually mass/time or volume/time for flow rate.

Temp' Difference = 26 - 15 degs = 11 degs
Mass of water = 1kg
Heat Capacity = 4200

Calculate the percentage of solar energy transferred to water.

Then, using the formula Q/t = -kA(temp diff/x)
Make a rough estimate of the temperature difference between top surface and bottom of aluminium sheet.

Any help would be great!

I suggest starting new separate threads for #'s 2, 3, and 4. That, and giving your thoughts on how to approach solving them. Again, it's just that you're more likely to get help that way.

Good luck.

 

[thomate1]

Question 1:
To find the r.m.s speed of all molecules when the Kelvin temperature has doubled, we can use the formula v = √(3kT/m), where v is the r.m.s speed, k is the Boltzmann constant, T is the temperature in Kelvin, and m is the molecular mass.

Since we know the r.m.s speed at the given temperature, we can set up the following equation:
1300 = √(3kT/4)

To solve for T, we first need to find the value of the Boltzmann constant. This can be found using the ideal gas law, PV = nRT, where P is pressure, V is volume, n is the number of moles, R is the gas constant, and T is the temperature in Kelvin. Rearranging this equation, we get:
k = (PV)/(nT)

Plugging in the given values, we get:
k = (900000 * 5*10^-3)/(2 * 8*10^-3 * 300) = 0.75

Now we can solve for T:
1300 = √(3 * 0.75 * T/4)
T = (1300^2 * 4)/(3 * 0.75) = 693333.33 K

To find the r.m.s speed at double the temperature, we simply double the temperature and plug it back into the formula:
v = √(3 * 0.75 * 1386666.67/4) = 1699.03 m/s

Question 2:
To show the equivalent formula, we can start by rearranging the ideal gas equation, PV = nRT, to solve for n:
n = PV/RT

Then, we plug this into the kinetic theory formula, pV = (1/3)nmc^2, and simplify:
pV = (1/3)(PV/RT)mc^2
pV = (1/3)(PV/T)(1/2)mc^2
pV = (1/2)(PV/T)mc^2

Since U = (3/2)nRT, we can substitute PV/RT for n and simplify:
U = (3/2)(PV/RT)RT
U = (3/2)PV

Since PV = NkT, we can substitute this into the