Final answer:
To calculate the internal energy of the gas, one must use the formula U = (3/2)nRT. The number of moles is 5 (since it's five times Avogadro's number), and after converting the temperature to Kelvin, one can find the internal energy by solving the equation with the known constants.
Step-by-step explanation:
The student is looking to find the internal energy of a gas within a sealed cubical container. To solve this, the ideal gas law and the formula for the internal energy of a monatomic gas can be used. Since neon is a monatomic gas, the internal energy (U) is given by the formula U = (3/2)nRT, where n is the number of moles of the gas, R is the ideal gas constant (8.314 J/(mol·K)), and T is the absolute temperature in Kelvin.
Given that the gas has five times Avogadro's number of atoms, we can determine the number of moles (since one mole contains Avogadro's number of atoms). The temperature given in degrees Celsius must be converted to Kelvin by adding 273.15. Hence, the temperature in Kelvin is 28.0°C + 273.15 = 301.15 K.
Now, we can calculate the number of moles as follows:
- Number of moles (n) = 5 × Avogadro's number / Avogadro's number per mole = 5 moles
- Internal energy (U) = (3/2) × 5 × 8.314 J/(mol·K) × 301.15 K
The above calculations will give us the internal energy in Joules.