According to Boyle’s law, the volume V of a gas varies inversely to the pressure P exerted by the gas. The volume of a given gas under a pressure of 32 kg per cm2 is 200 cm3. What will be the volume of this gas when the pressure exerted is 40 kg per cm2?
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To solve this problem, we can use Boyle's law, which states that the volume V of a gas varies inversely to the pressure P.
Boyle's law can be represented by the formula:
V₁ * P₁ = V₂ * P₂
where:
V₁ = initial volume
P₁ = initial pressure
V₂ = final volume
P₂ = final pressure
Given:
V₁ = 200 cm³ (initial volume)
P₁ = 32 kg/cm² (initial pressure)
P₂ = 40 kg/cm² (final pressure)
Let's substitute these values into the formula:
200 cm³ * 32 kg/cm² = V₂ * 40 kg/cm²
Simplifying the equation:
6400 kg/cm² = V₂ * 40 kg/cm²
Now, let's solve for V₂ by dividing both sides of the equation by 40 kg/cm²:
V₂ = 6400 kg/cm² / 40 kg/cm²
V₂ = 160 cm³
Therefore, the volume of the gas when the pressure exerted is 40 kg/cm² will be 160 cm³.
To solve this problem, we can use Boyle's law, which states that the volume of a gas is inversely proportional to the pressure exerted by the gas. In mathematical terms, this relationship can be written as:
V₁P₁ = V₂P₂
where V₁ and P₁ are the initial volume and pressure, and V₂ and P₂ are the final volume and pressure.
Given:
V₁ = 200 cm³
P₁ = 32 kg/cm²
P₂ = 40 kg/cm²
To find V₂, we can rearrange the equation:
V₂ = (V₁ * P₁) / P₂
Plugging in the given values:
V₂ = (200 cm³ * 32 kg/cm²) / 40 kg/cm²
Now, let's solve for V₂:
V₂ = (6400 cm²·kg) / 40 kg/cm²
V₂ = 160 cm³
Therefore, the volume of the gas when the pressure is 40 kg/cm² is 160 cm³.
PV=k, so you want V such that
40V = 32*200