Finding Temperature Using Ideal Gas Law

In summary, the pressure in a constant-volume gas thermometer is 7.09x10 to the fifth power Pa at 100.0 degrees celsius and 5.19 x 10 to the fourth power Pa at 0.0 degrees celsius. When the pressure is 4.05x10 to the third power Pa, the temperature is 100.5 degrees celsius.
  • #1
LezardValeth
13
0
The pressure in a constant-volume gas thermometer is 7.09x10 to the fifth power Pa at 100.0 degrees celsius and 5.19 x 10 to the fourth power Pa at 0.0 degrees celsius. What is the temperature when the pressure is 4.05x10 to the third power Pa?

now I've been told how to do this problem many different ways (those sources arent reliable) then I went to my teacher and she said to find the volume and use PV=nRT

ok so I know what R is and in order to use PV=nRT don't I have to find moles?

Im just completely confuse atm
 
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  • #2
LezardValeth said:
The pressure in a constant-volume gas thermometer is 7.09x10 to the fifth power Pa at 100.0 degrees celsius and 5.19 x 10 to the fourth power Pa at 0.0 degrees celsius. What is the temperature when the pressure is 4.05x10 to the third power Pa?
now I've been told how to do this problem many different ways (those sources arent reliable) then I went to my teacher and she said to find the volume and use PV=nRT
ok so I know what R is and in order to use PV=nRT don't I have to find moles?
Im just completely confuse atm


Yes, and no.

The trick is, there are two states here, both with the same n that are given to you. So make a system of two equations using PV=nRT and the first two states given. Then you have two equations with two unknowns, V and n. Solve for both, then use PV=nRT for the third state to answer the question.
 
  • #3
[tex]\frac{P}{T} = \frac{n R}{V} = constant[/tex]

[tex]\frac{P_1}{T_1} = \frac{P_2}{T_2}[/tex]

[tex]T_2 = \frac{P_2 T_1}{P_1}[/tex]

That clear anything up? Just notice that when some combination of variables is constant, you can equate them during different conditions to solve for an unknown.
 
Last edited:
  • #4
durt said:
[tex]\frac{P}{T} = \frac{n R}{V} = constant[/tex]
[tex]\frac{P_1}{T_1} = \frac{P_2}{T_2}[/tex]
[tex]T_2 = \frac{P_2 T_1}{P_1}[/tex]
That clear anything up? Just notice that when some combination of variables is constant, you can equate them during different conditions to solve for an unknown.

Im not quite sure about the first equation (math isn't my strong point sorry >< )
 
  • #5
I just rearranged the ideal gas equation, and since the number of moles and the volume don't change, its constant.
 
  • #6
so if n and V are constant that formula would become P over T = R ?
 
  • #7
LezardValeth said:
so if n and V are constant that formula would become P over T = R ?

No. Look at my post. Durt did the same thing, he just showed the equations rather than talking about why it worked so much.
 
  • #8
They're not necessarily 1 (and even if they were, the units would be different from those of R). You can't know what the constant is because you don't know n or V. All you know is that P/T is always constant. If P gets bigger, T gets bigger. If T gets smaller, P gets smaller.
 
  • #9
thanks a lot guys I appreciate the help

Ill try to figure this out with the info you guys gave me =]
 

1. What is an ideal gas?

An ideal gas is a theoretical gas composed of particles that have no volume and do not interact with each other. This means that they do not experience any attraction or repulsion between particles, and they also do not have any volume or size.

2. How is temperature related to ideal gas?

Temperature is directly related to the average kinetic energy of the particles in an ideal gas. As temperature increases, the particles move faster and have a higher average kinetic energy. In an ideal gas, this relationship is described by 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 temperature.

3. What is absolute zero and how does it relate to ideal gas temperature?

Absolute zero is the lowest possible temperature, at which all molecular motion stops. In an ideal gas, this would mean that the particles have no kinetic energy and do not move at all. Absolute zero is important in the ideal gas law because it is the theoretical point at which the volume of an ideal gas would be zero.

4. How does an increase in temperature affect the volume of an ideal gas?

According to the ideal gas law, an increase in temperature would result in an increase in volume, assuming pressure and the number of moles remain constant. This is because the average kinetic energy of the particles increases with temperature, causing them to move faster and take up more space.

5. Can an ideal gas have a negative temperature?

No, an ideal gas cannot have a negative temperature. Absolute zero is the lowest possible temperature and cannot be negative. In addition, the ideal gas law does not allow for negative temperatures, as it would result in a negative volume, which is physically impossible.

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