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

[BadlyAddicted]

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?

 

[Doc Al]

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?

 

[thomate1]

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.