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ankoles [38]
2 years ago
13

How to calculate the unknown force

Physics
1 answer:
Lesechka [4]2 years ago
5 0

the formula to calculate the force is, F = MA

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A gas occupies a volume of 1.0 m3 in a cylinder at a pressure of 120kPa. A piston compresses the gas until the volume is 0.25m3,
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Approximately 480\; \rm kPa, assuming that this gas is an ideal gas.

Explanation:

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  • Let V(\text{Final}) and P(\text{Final}) denote the volume and pressure of this gas after the compression.

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\displaystyle \frac{P(\text{Final})}{P(\text{Initial})} = \frac{V(\text{Initial})}{V(\text{Final})}.

Note that in Boyle's Law, P is inversely proportional to V. Therefore, on the two sides of this equation, "final" and "initial" are on different sides of the fraction bar.

For this particular question:

  • V(\text{initial}) = 1.0\; \rm m^3.
  • P(\text{Initial}) = 120\; \rm kPa.
  • V(\text{final}) = 0.25\; \rm m^3.
  • The pressure after compression, P(\text{Final}), needs to be found.

Rearrange the equation to obtain:

\displaystyle P(\text{Final}) = \frac{V(\text{Initial})}{V(\text{Final})} \cdot P(\text{Initial}).

Before doing any calculation, think whether the pressure of this gas will go up or down. Since the gas is compressed, collisions between its particles and the container will become more frequent. Hence, the pressure of this gas should increase.

\begin{aligned}P(\text{Final}) &= \frac{V(\text{Initial})}{V(\text{Final})} \cdot P(\text{Initial})\\ &= \frac{1.0\; \rm m^{3}}{0.25\; \rm m^{3}} \times 120\; \rm kPa = 480\; \rm kPa\end{aligned}.

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