The image shows a piston system where gas is compressed. If the uncompressed system is at a standard pressure of 1 atm, what is the pressure of the compressed piston
The Correct Answer and Explanation is:
To accurately determine the pressure of a compressed piston system, we must apply the principles of Boyle’s Law, which states:
P₁V₁ = P₂V₂
Where:
- P₁ = Initial pressure (1 atm)
- V₁ = Initial volume
- P₂ = Final (compressed) pressure
- V₂ = Final (compressed) volume
Since the image itself is not provided here, we can only give a general approach. However, Boyle’s Law implies that if the volume of the gas in the piston is reduced, the pressure increases proportionally, assuming the temperature remains constant and the gas behaves ideally.
Example Calculation:
Suppose:
- Initial pressure, P₁ = 1 atm
- Initial volume, V₁ = 1.0 L
- Final volume after compression, V₂ = 0.25 L
Using Boyle’s Law:
P₂ = (P₁ × V₁) / V₂
P₂ = (1 atm × 1.0 L) / 0.25 L = 4 atm
So, the final pressure is 4 atm.
Explanation:
The pressure in a compressed piston system increases due to the reduction in volume, governed by Boyle’s Law, a fundamental gas law in thermodynamics. This law describes the inverse relationship between pressure and volume for a fixed amount of gas at constant temperature. When the piston compresses the gas, its volume decreases. Since the gas molecules have less space to move around, they collide more frequently with the walls of the container, which results in an increase in pressure.
For instance, if the volume is compressed to a quarter of its original size and the starting pressure was 1 atmosphere, the pressure becomes four times greater — 4 atmospheres. This inverse relationship is mathematically expressed as P₁V₁ = P₂V₂, where P and V represent pressure and volume respectively.
It’s important to note that this relationship holds true under ideal gas behavior — which assumes no intermolecular forces and that the volume occupied by the gas particles themselves is negligible. In real-world applications, deviations might occur at very high pressures or low temperatures, but for many practical purposes, Boyle’s Law gives an accurate estimate.
Thus, when observing a compressed piston system where the initial pressure is 1 atm and the volume is significantly reduced, the final pressure can be estimated using this principle. The more the volume is compressed, the higher the pressure becomes, helping engineers design safe and effective mechanical systems.
