If a gas of volume 6000 cm3 and pressure of 100 Kpa is compressed quasistatically according to PV2 = constant until the volume becomes 2000 cm3. Determine the final pressure.
900 Kpa
Understanding the behavior of gases under different conditions is a fundamental concept in thermodynamics and physics. This problem involves a gas undergoing a quasistatic compression, which is a process that happens slowly enough for the system to remain in equilibrium at all times. The specific relationship governing this compression is given by \(PV^2 = \text{constant}\).
Gas Compression Problem Overview
The question asks us to determine the final pressure of a gas given its initial volume and pressure, and its final volume, under a specific compression law. This type of problem requires applying the given gas law to relate the initial and final states of the gas.
Pressure and Volume Initial Conditions
Let's first list down the initial conditions and the given final volume for the gas compression:
| Parameter | Symbol | Value |
|---|---|---|
| Initial Volume | \(V_1\) | 6000 cm3 |
| Initial Pressure | \(P_1\) | 100 kPa |
| Final Volume | \(V_2\) | 2000 cm3 |
We need to find the final pressure, \(P_2\), after the gas is compressed quasistatically.
Quasistatic Compression Formula
The problem states that the gas is compressed quasistatically according to the relationship \(PV^2 = \text{constant}\). This means that the product of the pressure and the square of the volume remains constant throughout the compression process. Therefore, we can write the relationship between the initial state (1) and the final state (2) as:
\[P_1V_1^2 = P_2V_2^2\]Our goal is to determine \(P_2\), the final pressure, so we can rearrange this equation to solve for \(P_2\):
\[P_2 = P_1 \left(\frac{V_1}{V_2}\right)^2\]Final Pressure Calculation Steps
Now, let's substitute the given values into the derived formula to calculate the final pressure of the gas.
- Identify Given Values:
- Initial Pressure (\(P_1\)) = 100 kPa
- Initial Volume (\(V_1\)) = 6000 cm3
- Final Volume (\(V_2\)) = 2000 cm3
- Apply the Quasistatic PV2 Constant Relation:
Using the derived formula for the final pressure:
\[P_2 = P_1 \left(\frac{V_1}{V_2}\right)^2\] - Substitute and Calculate:
Substitute the numerical values into the equation:
\[P_2 = 100 \text{ kPa} \times \left(\frac{6000 \text{ cm}^3}{2000 \text{ cm}^3}\right)^2\]First, simplify the ratio of the volumes:
\[\frac{6000}{2000} = 3\]Next, square this ratio:
\[(3)^2 = 9\]Finally, multiply the initial pressure by this squared ratio to find the final pressure:
\[P_2 = 100 \text{ kPa} \times 9\] \[P_2 = 900 \text{ kPa}\]
Thus, the final pressure of the gas after quasistatic compression is 900 kPa.
Important Questions from Thermodynamics System and Processes
- In a polytropic process described by $PV^n = C$, if the polytropic index $n$ is equal to zero, then the process is characterized by constant
Why do particles in liquid water at 0°C have more energy as compared to particles in ice at the same temperature?
Choose the INCORRECT option for the process and its work done (W) and heat transfer (Q) relations.
For a closed system. identify the processes where the following quantities are zero.
1. Heat
2. Work done
3. Internal Energy
Identify the CORRECT statement with respect to the magnitudes of different quantities for different thermodynamic processes.
