When the temperature stays the same, the volume of gas is inversely proportional to the pressure of the gas. If a balloon is filled with 228 cubic inches of a gas at a pressure of 14 pounds per square inch, find the new pressure of the gas if the volume is decreased to 38 cubic inches.

84 pounds per square inch

Step-by-step explanation:

Given:

Initial volume V1 = 228 cubic inches

Initial pressure P1=14 pounds per square inch

Final volume V2=38 cubic inches

Required:

Final pressure P2=?

According to the Boyle's law, the pressure of a given mass of an ideal gas is inversely proportional to its volume at a constant temperature.

P1 V1 = P2 V2

P2 = (P1 x V1) / V2

P2 = (14 x 228) / 38

P2 = 84 pounds per square inch

Therefore, the new pressure of the gas is 84 pounds per square inch

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