Final answer:
To calculate the force the gas exerts on the box's sides, we use the ideal gas law, calculate the pressure for each temperature, and then use that pressure with the box side's area to find the force. The temperature is first converted to Kelvin, the ideal gas law is applied to find the pressure, and this pressure is multiplied by one side's area.
Step-by-step explanation:
To determine the force exerted by the gas on each side of a rigid cubical box, we can use the ideal gas law, which is PV = nRT. For both parts of the question, we'll calculate the pressure first and then use it to calculate the force on a single side of the box.
(a) First, we convert the temperature from Celsius to Kelvin: T1 = 20.0°C = 293.15 K. The ideal gas law rearranged for pressure gives us P = nRT/V. The volume of the cubical box, V, is 0.300 m × 0.300 m × 0.300 m = 0.027 m³. With R = 8.314 J/(mol·K), the pressure P is calculated as follows:
P = (3 mol) × (8.314 J/(mol·K)) × (293.15 K) / (0.027 m³)
Next, we calculate the force exerted on one side of the box using the pressure and the area of a side: F = P × A, where A = 0.300 m × 0.300 m.
(b) For the increased temperature of T2 = 100.0°C = 373.15 K, we repeat the process to find the new pressure P, using the same volume and R value.
P = (3 mol) × (8.314 J/(mol·K)) × (373.15 K) / (0.027 m³)
Again, we use the formula F = P × A to determine the force on one side of the box at this higher temperature.