Final answer:
By applying Boyle's Law to a gas with an initial volume of 4 m³ and pressure of 200 kPa, the pressure when the volume is reduced to 3 m³ is calculated to be 266.67 kPa, assuming constant temperature.
Step-by-step explanation:
Calculating Pressure Change in a Gas at Constant Temperature
When dealing with the relationship between the pressure and volume of a gas at a constant temperature, we can utilize Boyle's Law. This law indicates that the pressure of a gas is inversely proportional to its volume when the temperature is kept constant. In mathematical terms, Boyle's Law is expressed as P1 * V1 = P2 * V2, where P1 and V1 are the initial pressure and volume, and P2 and V2 are the conditions after the change.
In this problem, initially, we have a gas volume of 4 m³ at a pressure of 200 kPa. To find the new pressure when the volume changes to 3 m³, we rearrange the equation to P2 = P1 * V1 / V2. So, P2 = (200 kPa) * (4 m³) / (3 m³). By performing the multiplication and division, we find P2 = 266.67 kPa.
The pressure of the gas when its volume is reduced to 3 m³ at the same temperature is 266.67 kPa, assuming temperature and amount of gas remain unchanged.