Figure 8.1 Piston seals off a cylindrical container of oxygen.
-In Fig. 8.1, a piston of cross-sectional area 1 m² seals a cylinder of gas, of length 0.5 m, at atmospheric pressure (so that there is no net force on the piston) . The gas is at the ambient temperature of 20°C, then the gas is heated to 100°C. What extra force must the piston exert to contain the gas in the cylindrical space of reduced length 0.4 m?

Question

Figure 8.1

Piston seals off a cylindrical container of oxygen.
-In Fig. 8.1, a piston of cross-sectional area 1 m² seals a cylinder of gas, of length 0.5 m, at atmospheric pressure (so that there is no net force on the piston) . The gas is at the ambient temperature of 20°C, then the gas is heated to 100°C. What extra force must the piston exert to contain the gas in the cylindrical space of reduced length 0.4 m?

Quizplus · Accepted Answer

The force exerted by the piston is determined by the pressure difference it creates. When the gas is heated, its pressure increases due to the combined effects of increased temperature and decreased volume. Using the ideal gas law, $PV = nRT$, where $P$ is pressure, $V$ is volume, $n$ is the amount of gas, $R$ is the ideal gas constant, and $T$ is temperature in Kelvin, we can calculate the change in pressure. Since the volume decreases from 0.5 m to 0.4 m (a reduction to 80% of the original volume) and the temperature increases from 20°C (293K) to 100°C (373K), the final pressure will be higher. The force is the pressure difference times the area, $F = \Delta P \times A$. Given that the area is 1 m², and assuming the initial pressure is atmospheric and there's no net force initially, the extra force is due to the increased pressure from heating and compressing the gas. The exact calculation would involve finding the new pressure using the ideal gas law and then calculating the force from the pressure difference. The correct answer involves understanding these principles and applying them to find that the extra force is $6.0 \times 10^{4} N$.

Figure 81 Piston Seals Off a Cylindrical Container of Oxygen