A cylinder containing 100.9 cubic centimeter of gas at a pressure of 376 kPa when its temperature is 534 K. Given that its temperature is unchanged when the pressure was increased by a factor of 5.9, Determine the new volume of the gas (In cubic centimeter).
Kinetic Theory of Gas
The Kinetic Theory of gases is a classical model of gases, according to which gases are composed of molecules/particles that are in random motion. While undergoing this random motion, kinetic energy in molecules can assume random velocity across all directions. It also says that the constituent particles/molecules undergo elastic collision, which means that the total kinetic energy remains constant before and after the collision. The average kinetic energy of the particles also determines the pressure of the gas.
P-V Diagram
A P-V diagram is a very important tool of the branch of physics known as thermodynamics, which is used to analyze the working and hence the efficiency of thermodynamic engines. As the name suggests, it is used to measure the changes in pressure (P) and volume (V) corresponding to the thermodynamic system under study. The P-V diagram is used as an indicator diagram to control the given thermodynamic system.
![### Problem Statement: Calculation of Gas Volume in a Cylinder
A cylinder containing 100.9 cubic centimeters of gas is at a pressure of 376 kPa when its temperature is 534 K. Given that its temperature is unchanged when the pressure was increased by a factor of 5.9, determine the new volume of the gas (in cubic centimeters).
**Note:** Your answer must be in cubic centimeters; however, do not include the unit, just enter the magnitude that corresponds to the final volume in cubic centimeters. Round your answer to 2 decimal points.
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To solve this problem, you can use the ideal gas law and the relationship between pressure and volume at constant temperature (Boyle's Law). The pressure-volume relationship is given by:
\[ P_1 V_1 = P_2 V_2 \]
Where:
- \( P_1 \) = Initial pressure = 376 kPa
- \( V_1 \) = Initial volume = 100.9 cm³
- \( P_2 \) = Final pressure = \( 376 kPa \times 5.9 \)
- \( V_2 \) = Final volume (to be determined)
Rearrange the equation to solve for \( V_2 \):
\[ V_2 = \frac{P_1 V_1}{P_2} \]
Calculate the new volume using the given data and the formula. Make sure to round your answer to 2 decimal points.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7f1e4f7e-3ee3-4328-9071-c5dd7af83341%2Fabfbda7b-6279-4a52-b428-f261fdb84a15%2F6i0d95x_processed.jpeg&w=3840&q=75)
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