**Correct Option: C. T is increased and P is decreased** ### Detailed Explanation: To understand why option C is correct, we need to refer to the ideal gas law, which is expressed as: \[ PV = nRT \] Where: - \( P \) = pressure of the gas - \( V \) = volume of the gas - \( n \) = number of moles of gas - \( R \) = ideal gas constant - \( T \) = temperature of the gas (in Kelvin) From this equation, we can see that the volume \( V \) of a gas is directly proportional to the temperature \( T \) and inversely proportional to the pressure \( P \). This means: - If the temperature increases (while keeping pressure constant), the volume will increase. - If the pressure decreases (while keeping temperature constant), the volume will also increase. Now, let’s analyze the conditions in option C: 1. **T is increased**: When the temperature of the gas inside the balloon increases, the kinetic energy of the gas molecules increases. This causes the molecules to move faster and collide with the walls of the balloon more forcefully, leading to an increase in volume. 2. **P is decreased**: When the pressure exerted on the gas decreases, the gas molecules have more space to expand. This reduction in pressure allows the gas to occupy a larger volume, as there are fewer external forces compressing the gas. Combining these two effects, increasing the temperature while decreasing the pressure will lead to a significant increase in the volume of the balloon. ### Why the Other Options are Incorrect: **A. P and T are increased**: - Increasing both pressure and temperature does not guarantee an increase in volume. While increasing temperature would increase volume, increasing pressure would counteract this effect. The net effect on volume is uncertain and likely to decrease or remain constant, depending on the relative magnitudes of the changes. **B. Both T and P are decreased**: - Decreasing temperature would lead to a decrease in volume because the kinetic energy of the gas molecules would decrease, causing them to collide less forcefully with the walls of the balloon. Decreasing pressure would increase volume, but the effect of decreasing temperature would dominate, leading to an overall decrease in volume. **D. T is decreased and P is increased**: - Decreasing temperature reduces the kinetic energy of the gas molecules, leading to a decrease in volume. Increasing pressure further compresses the gas, which would also decrease the volume. Both changes work against increasing volume, making this option incorrect. ### Summary of Key Points: - The ideal gas law \( PV = nRT \) shows the relationship between pressure, volume, and temperature. - Increasing temperature increases volume due to higher kinetic energy of gas molecules. - Decreasing pressure allows gas to expand, increasing volume. - Option C (T increased, P decreased) leads to an increase in volume, while the other options either decrease volume or have an uncertain effect. This understanding of gas behavior is crucial for predicting how changes in temperature and pressure affect the volume of gases in various scenarios, such as in balloons or other gas-filled containers.