Ideal Gas Law Gas in a Piston Problem

In summary, the gas in the piston initially has a temperature of 25 degrees celsius and a volume of 4.0L at atmospheric pressure. The temperature is then increased to 193 degrees celsius, causing the piston to expand to its maximum volume. When the pressure in the room is increased to 4.3 atm, the new volume of the piston at a constant temperature of 193 degrees celsius is 1.5L.
  • #1
maceng7
18
0

Homework Statement


A gas is in a piston which is at 25 degrees celsius with a volume 4.0L is held in a room at atmospheric pressure. If the temperature is increased to 193 degrees celsius, the piston expands to it's maximum volume. If the pressure in the room is then increased to 4.3 atm, what is the new volume of the piston (temperature remains at 193 degrees celsius)?

T1 = 25 = 298.15K

V1 = 4.00L

P1 = 1.000atm

P2 = 4.3 atm

T2 = 466.15K

V2 = ?


Homework Equations



P1V1 / T1 = P2V2 / T2

The Attempt at a Solution



P1V1 / T1 = P2V2 / T2

V2 = P1V1T2 / T1P2

V2 = (1.000atm)(4.0L)(466.15K) / (298.15K)(4.3atm)

= 1.45L
= 1.5L

Just want someone to check my solution
 
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  • #2
Looks correct.
 

1. What is the Ideal Gas Law and how does it relate to gas in a piston problems?

The Ideal Gas Law is a fundamental equation in thermodynamics that describes the behavior of an ideal gas. It states that the pressure, volume, and temperature of an ideal gas are all directly proportional to each other. In gas in a piston problems, this law is used to calculate the changes in pressure, volume, and temperature of a gas as it is compressed or expanded in a piston.

2. What are the units for pressure, volume, and temperature in the Ideal Gas Law?

Pressure is typically measured in units of Pascals (Pa) or atmospheres (atm), volume is measured in cubic meters (m3), and temperature is measured in Kelvin (K). However, for convenience, other units such as milliliters (mL) and Celsius (°C) can also be used as long as they are converted to the appropriate units.

3. How can the Ideal Gas Law be manipulated to solve for different variables?

The Ideal Gas Law can be rearranged into different forms to solve for different variables. For example, if the temperature is held constant, the law can be written as P1V1 = P2V2, where P1 and V1 represent the initial pressure and volume, and P2 and V2 represent the final pressure and volume. Similarly, if the pressure is held constant, the law can be written as V1/T1 = V2/T2, where T1 and T2 represent the initial and final temperatures.

4. What are the assumptions made in the Ideal Gas Law?

The Ideal Gas Law assumes that the gas being studied is an ideal gas, meaning that it follows the laws of kinetic theory and has no intermolecular forces. It also assumes that the gas particles have negligible volume and that the gas is in thermal equilibrium.

5. How accurate is the Ideal Gas Law in real-world situations?

The Ideal Gas Law is most accurate for gases at low pressures and high temperatures. At higher pressures and lower temperatures, the gas particles may deviate from ideal behavior, so more complex equations must be used. Additionally, the Ideal Gas Law does not take into account factors such as non-ideal interactions between gas particles or the presence of real-world imperfections in piston systems, so it may not be perfectly accurate in these situations.

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