Solving Gas Pressure Law: 4.5*10^5Pa to 1*10^5Pa

In summary, the initial pressure of a mass of dry gas in a rigid vessel is 4.5*10^5Pa. The volume of the vessel is 0.1m^3 and it is connected to a vacuum pump with a volume of 0.005m^3. Using the formula P_1*V_1 = P_2*(0.1 + n(0.005)), where n is the number of strokes, the correct answer for the number of strokes necessary to reduce the gas pressure from 4.5*10^5Pa to 1*10^5Pa is 31. This is due to the incorrect use of the equation for multiple strokes. The correct fraction by which the
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the intiial pressure of a mass of dry gas in a rigid vessel is 4.5*10^5Pa. The volume of the vessel is 0.1m^3. It is connected to a vacuum pump, whih consists of a cylinder fitted with a piston. The pump cylinder has a volume of 0.005m^3. i am supposed to determine the number of strokes necessary to reduce the gas pressure to 1*10^5Pa

i used the formula: P_1*V_1 = P_2*(0.1 + n(0.005)), where n is the number of strokes
P_1 = 4.5*10^5, V_1 = 0.1, P_2 = 1*10^5.

the answer i got is 70 strokes, which according to the book is incorrect. The answer on the book is 31. however, when i substiute 31 instead of n, P_2 is not equal to 1*10^5 Pascals, it is however when i substitute n=70. I'm not sure whether it's a mistake in the book, but i think it is. the first part of the question asks me to find the pressure after 2 strokes. when i substitute 2 in my equation, i get the pressure that he asked for so I'm pretty sure the equation is not wrong.

can someone show me where I'm mistaken please?
 
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  • #2
The book is correct. Your equation is mistaken--it's only correct for a single stroke. (As long as the number of strokes is small it's approximately correct, which explains you getting an OK answer for 2 strokes.)

Answer this: With every stroke the pressure is reduced by what fraction?
 
  • #3


As a scientist, it is important to always check your calculations and assumptions to ensure accuracy. In this case, it seems that your calculations are correct and the book's answer may be incorrect. However, it is also possible that there is a mistake in the question or in the units used. I would suggest double checking your calculations and also checking with your instructor or a colleague to see if they have any insights on the discrepancy. It is also possible that the textbook may have a correction or errata section where this question may be addressed. In any case, it is important to communicate any discrepancies or errors to ensure accurate understanding and learning.
 

Related to Solving Gas Pressure Law: 4.5*10^5Pa to 1*10^5Pa

1. What is the gas pressure law?

The gas pressure law, also known as Boyle's Law, states that the pressure of a gas is inversely proportional to its volume when temperature is held constant. This means that as the volume of a gas decreases, its pressure increases, and vice versa.

2. How do you solve for gas pressure?

To solve for gas pressure, you need to know the volume and temperature of the gas. Then, you can use the ideal gas law (PV = nRT) to calculate the pressure. In this case, you would use the given pressure values and solve for the unknown variable, either volume or temperature.

3. What are the units for gas pressure?

The SI unit for gas pressure is pascal (Pa), which is equivalent to one newton per square meter. Other commonly used units include atmospheres (atm), millimeters of mercury (mmHg), and pounds per square inch (psi).

4. How do you convert between different units of gas pressure?

To convert between different units of gas pressure, you can use conversion factors. For example, to convert from atmospheres to pascals, you would multiply the value in atmospheres by 101325 (atm to Pa conversion factor). You can also use online conversion tools or consult a gas pressure conversion chart.

5. What is the significance of the given pressure values (4.5*10^5Pa to 1*10^5Pa)?

The given pressure values represent a change in pressure from 4.5*10^5Pa to 1*10^5Pa, which is a decrease in pressure by a factor of 4.5. This could represent a change in volume, temperature, or both, depending on the context of the problem. It is important to note that gas pressure is highly dependent on these factors and can change significantly with small variations in volume or temperature.

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