Question

A closed piston/cylinder device contains 0.5 kg of air initially at 300 K and 100 kPa. The air is

now slowly compressed in an isothermal process to a final pressure of 250 kPa.
(a) Determine the volume in m3 of the air at the initial state.
(b) Determine the temperature in K of the air at the final state.
(c) Determine the volume in m3 of the air at the final state.

Answer 1

The volume of the air at the initial state is determined using the ideal gas law equation. The temperature of the air at the final state remains constant. The volume of the air at the final state is also determined using the ideal gas law equation.

Step-by-step explanation:

(a) To determine the volume in m3 of the air at the initial state, we can use the ideal gas law equation: PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the gas constant, and T is the temperature. Rearranging the equation to solve for V, we get V = nRT/P. Plugging in the given values, we have V = (0.5 kg * 8.314 J/(mol*K) * 300 K) / (100,000 Pa).

(b) To determine the temperature in K of the air at the final state, we can use the ideal gas law equation again. Since the process is isothermal, the temperature will remain constant. Therefore, the temperature at the final state is also 300 K.

(c) To determine the volume in m3 of the air at the final state, we can use the ideal gas law equation. Rearranging the equation to solve for V, we get V = nRT/P. Plugging in the given values, we have V = (0.5 kg * 8.314 J/(mol*K) * 300 K) / (250,000 Pa).