Final answer:
To find the pressure change of a gas heated at constant volume, we use the ideal gas law. The pressure increases from 14.7 psi to approximately 17.8 psi, resulting in a pressure change of about 3.1 psi when the temperature is raised from 200°C to 300°C.
Step-by-step explanation:
The pressure change of a gas when heated at a constant volume can be found using the ideal gas law, which is PV = nRT. However, the information given and the problem analysis suggest that Charles's Law is being mistakenly used instead of the ideal gas law since the question asks about pressure change, not volume change, at constant volume due to a temperature increase. To correct this, we must apply the ideal gas law for constant volume processes.
Assuming one mole of gas for simplicity, the relationship for constant volume becomes: \(P1/T1 = P2/T2\) where P1 and T1 are the initial pressure and temperature, and P2 and T2 are the final pressure and temperature, respectively. To convert Celsius to Kelvin, add 273.15 to the Celsius temperature. Therefore, T1 is 200 + 273.15 = 473.15 K, and T2 is 300 + 273.15 = 573.15 K.
Plugging in the values, \(14.7 psi/473.15 K = P2/573.15 K\), solving for \(P2\) we find that the final pressure P2 is about 17.8 psi. Therefore, the pressure change is approximately 3.1 psi.