Question

Suppose that a cylinder starts out at a volume of 1.27 x 10⁻4 m³ and a pressure of 126 Pa. Assuming an isothermal process, find the pressures for the following volumes.

a) 1.27 x 10⁻4 m³ (initial volume)
b) 2.54 x 10⁻4 m³
c) 6.35 x 10⁻5 m³
d) 3.18 x 10⁻5 m³

Answer 1

To find the pressures for the given volumes, we can use the initial volume and pressure to solve for the constant k in the equation: P₁V₁ = k. Then, we can substitute the values of the final volumes to find the corresponding pressures.

Step-by-step explanation:

In an isothermal process, the pressure and volume of an ideal gas are inversely proportional at constant temperature. This means that as the volume of the gas decreases, the pressure increases, and vice versa.

This relationship can be expressed using Boyle's Law: P₁V₁ = P₂V₂, where P₁ and V₁ are the initial pressure and volume, and P₂ and V₂ are the final pressure and volume.

To find the pressures for the given volumes, we can use the initial volume and pressure to solve for the constant k in the equation: P₁V₁ = k. Then, we can substitute the values of the final volumes to find the corresponding pressures.

a) For the initial volume of 1.27 x 10⁻⁴ m³, we have P₁V₁ = k ⟻ 126 Pa x 1.27 x 10⁻⁴ m³ = k ⟻ k = 0.1602.

b) For the volume of 2.54 x 10⁻⁴ m³, we can use the value of k to find the pressure: P₂ = k / V₂ ⟻ P₂ = 0.1602 / 2.54 x 10⁻⁴ m³ = 630 Pa.

c) For the volume of 6.35 x 10⁻⁵ m³, we can again use the value of k to find the pressure: P₃ = k / V₃ ⟻ P₃ = 0.1602 / 6.35 x 10⁻⁵ m³ = 2520 Pa.

d) For the volume of 3.18 x 10⁻⁵ m³, we can use the value of k to find the pressure: P₄ = k / V₄ ⟻ P₄ = 0.1602 / 3.18 x 10⁻⁵ m³ = 5040 Pa.