The volume of a certain quantity of gas is inversely proportional to its pressure. If its pressure is 1000 grams per square cm, when its volume is 3m³, what will the pressure be when the gas is compressed to a volume of 2m³?
(Thanks in advance in helping me here)
2P = 3*1000
To solve this problem, we can use the inverse variation formula which states that if two variables, in this case, volume (V) and pressure (P), are inversely proportional, their product remains constant:
V1 * P1 = V2 * P2
Let's assign the given values to the variables:
V1 = 3m³ (initial volume)
P1 = 1000 grams/cm² (initial pressure)
V2 = 2m³ (final volume)
P2 = unknown (final pressure)
By substituting the values into the equation, we can solve for P2:
(3m³) * (1000 g/cm²) = (2m³) * P2
Now, we need to make sure the units are consistent. We can convert grams per square cm to a more standard unit of pressure, such as pascals (Pa).
Since 1 gram/cm² = 98.0665 pascals, we can convert the initial pressure:
P1 = 1000 g/cm² = 1000 * 98.0665 Pa ≈ 98066.5 Pa
Plugging in the values:
(3m³) * (98066.5 Pa) = (2m³) * P2
Now, we can solve for P2:
P2 = (3m³ * 98066.5 Pa) / (2m³)
P2 = (294199.5 m³*Pa) / (2m³)
P2 ≈ 147099.75 Pa
Therefore, when the gas is compressed to a volume of 2m³, the pressure will be approximately 147099.75 Pa.