Answer:
84 pounds per square inch
Step-by-step explanation:
Extracting the key information from the question:
*** Volume of a gas is inversely proportional to pressure of the gas.
*** A balloon is filled with 228 cubic inches of a gas at a pressure of 14 pounds per square inch.
*** Volume is then decreased to 38 cubic inches. we are required to find the new pressure of the gas.
Since volume is inversely proportional to pressure, then:
V = k × (1/p)
V = k/p
V = volume, p= pressure, k = mathematical constant
Since, V = 228 cubic inches, P = 14 pounds per square inches, k = ?
Substituting appropriately, we have:
228/1 = k/14
cross multiply
K = 228 × 14 = 3192
Using the same formula, we can calculate the new pressure of the gas since we know our mathematical constant and the volume it was decreased to.
V = k/p
Here, volume = 38, k = 3192
We now have:
38/1 = 3192/p
Cross multiply
38 × p = 3192
p = 3192/38
p = 84 pounds per square inch.
The new pressure of the gas after decrement of the volume= 84 pounds per square inch
When the temperature stays the same, the new pressure of the gas if the volume is decreased is 84 pounds per square inch.
Given the following data:
To find the new pressure of the gas if the volume is decreased:
Translating the word problem into a mathematical expression, we have;
[tex]V \alpha \frac{1}{P} \\\\V = \frac{k}{P}[/tex]
Where:
First of all, we would determine the constant of proportionality.
[tex]k = VP\\\\k = 228 \times 14[/tex]
k = 3,192
To find the new pressure:
[tex]P = \frac{k}{V} \\\\P = \frac{3192}{38}[/tex]
New pressure, P = 84 pounds per square inch
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