Calculating Gas Pressure: Solving for Pressure in a Variable Volume

In summary: If you do this, you can see that the pressure and volume of the gas in state 2 are the same as the pressure and volume of the gas in state 1, but the temperature is higher. If you keep shrinking the gas, the pressure and volume of the gas will stay the same, but the temperature will keep going up.
  • #1
Bechensten
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Homework Statement


Gas occupies 2m^3 at a pressure of 100kPa. What is the pressure when the volume is 1.5m^3 and the temprature is unchanged?

Homework Equations


p=nRT/V

The Attempt at a Solution


As a logic conclusion i took 1.5/2x100 and got 75 but 175 is not the answer.. The answer is 133kPa.
I also tried the p=nRT/V.
22.4l=1mol so 1500/22.4x1 is 66.96mol. (66.96x22.4x0)/1500=0
Can someone please tell me how to calculate this type of problem?

Thank you.
 
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  • #2
Bechensten said:

Homework Statement


Gas occupies 2m^3 at a pressure of 100kPa. What is the pressure when the volume is 1.5m^3 and the temprature is unchanged?

Homework Equations


p=nRT/V

The Attempt at a Solution


As a logic conclusion i took 1.5/2x100 and got 75 but 175 is not the answer.. The answer is 133kPa.
I also tried the p=nRT/V.
22.4l=1mol so 1500/22.4x1 is 66.96mol. (66.96x22.4x0)/1500=0
Can someone please tell me how to calculate this type of problem?

Thank you.
Well, your "logic conclusion" got warped somehow.

If you take a certain volume of gas and then shrink that volume, keeping the amount of gas and its temperature constant, what do you think happens to the pressure of the gas confined into that new, smaller volume?

If you analyze the relation PV = nRT, n is the same, R is a constant, and T is the same. So what happens to PV if V gets smaller?
 
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  • #3
Bechensten said:

Homework Statement


Gas occupies 2m^3 at a pressure of 100kPa. What is the pressure when the volume is 1.5m^3 and the temprature is unchanged?

Homework Equations


p=nRT/V

The Attempt at a Solution


As a logic conclusion i took 1.5/2x100 and got 75 but 175 is not the answer.. The answer is 133kPa.
I also tried the p=nRT/V.
22.4l=1mol so 1500/22.4x1 is 66.96mol. (66.96x22.4x0)/1500=0
Can someone please tell me how to calculate this type of problem?

Thank you.

Always check your units to make sure that what you are calculating makes sense.
You are analyzing the gas in two states.
Start with what you know. What is the pressure and volume of the gas in the first state? What do you know about the second state? I would encourage you to use subscripts. P1 is the pressure of the gas in state 1. P2 is the pressure of the gas in state 2. V1 is the volume of the gas in state 1. etc.
 
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FAQ: Calculating Gas Pressure: Solving for Pressure in a Variable Volume

1. How do you calculate gas pressure in a variable volume?

To calculate gas pressure in a variable volume, you can use the formula P = nRT/V, where P is pressure, n is the number of moles of gas, R is the gas constant, T is the temperature in Kelvin, and V is the volume.

2. What units are used for gas pressure?

Gas pressure is typically measured in units of Pascals (Pa), atmospheres (atm), millimeters of mercury (mmHg), or pounds per square inch (psi).

3. How does volume affect gas pressure?

In a closed container, as the volume of gas increases, the pressure decreases. This is because the molecules have more room to move around and exert less force on the container walls.

4. Can you solve for pressure if the volume is not constant?

Yes, using the ideal gas law, you can solve for pressure even if the volume is not constant. You would need to know the other variables, such as temperature, number of moles, and gas constant.

5. How does temperature affect gas pressure?

As temperature increases, gas molecules have more kinetic energy and move faster. This results in more frequent and forceful collisions with the container walls, leading to an increase in gas pressure. Similarly, as temperature decreases, gas pressure decreases.

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