Asked by Adivhaho muremi
4.2 A vessel of air with a volume of 0.25 m° at a pressure of 1.4 MPa, begin compressed to a pressure of 2.0 MPa, Caculate using Byiles law.
Answers
Answered by
GPT-4o mini
Boyle's Law states that for a given mass of gas at constant temperature, the pressure and volume of the gas are inversely proportional. This can be mathematically expressed as:
\[ P_1 V_1 = P_2 V_2 \]
Where:
- \( P_1 \) is the initial pressure,
- \( V_1 \) is the initial volume,
- \( P_2 \) is the final pressure,
- \( V_2 \) is the final volume.
Given:
- \( P_1 = 1.4 \) MPa
- \( V_1 = 0.25 \) m³
- \( P_2 = 2.0 \) MPa
We need to find \( V_2 \).
Using Boyle's Law, we can rearrange the equation to solve for \( V_2 \):
\[
V_2 = \frac{P_1 V_1}{P_2}
\]
Substituting the known values into the equation:
\[
V_2 = \frac{1.4 \, \text{MPa} \times 0.25 \, \text{m}^3}{2.0 \, \text{MPa}}
\]
Calculating:
\[
V_2 = \frac{1.4 \times 0.25}{2.0} = \frac{0.35}{2.0} = 0.175 \, \text{m}^3
\]
Thus, the final volume \( V_2 \) after compression to a pressure of 2.0 MPa is \( 0.175 \, \text{m}^3 \).
\[ P_1 V_1 = P_2 V_2 \]
Where:
- \( P_1 \) is the initial pressure,
- \( V_1 \) is the initial volume,
- \( P_2 \) is the final pressure,
- \( V_2 \) is the final volume.
Given:
- \( P_1 = 1.4 \) MPa
- \( V_1 = 0.25 \) m³
- \( P_2 = 2.0 \) MPa
We need to find \( V_2 \).
Using Boyle's Law, we can rearrange the equation to solve for \( V_2 \):
\[
V_2 = \frac{P_1 V_1}{P_2}
\]
Substituting the known values into the equation:
\[
V_2 = \frac{1.4 \, \text{MPa} \times 0.25 \, \text{m}^3}{2.0 \, \text{MPa}}
\]
Calculating:
\[
V_2 = \frac{1.4 \times 0.25}{2.0} = \frac{0.35}{2.0} = 0.175 \, \text{m}^3
\]
Thus, the final volume \( V_2 \) after compression to a pressure of 2.0 MPa is \( 0.175 \, \text{m}^3 \).