Final answer:
To calculate the internal energy of 15 mg of helium at 0°C, convert mass to moles, temperature to Kelvin, and use the internal energy formula for monatomic gases. However, the calculated internal energy is not among the provided options, suggesting there may be a mistake in the question or answer choices.
Step-by-step explanation:
To calculate the internal energy of 15 mg of helium at a temperature of 0°C, you first need to understand that the internal energy of an ideal gas is related to its temperature and the number of moles of the gas. For a monatomic ideal gas like helium, the internal energy U can be calculated using the formula:
U = (3/2) * n * RT
Where:
First, convert 15 mg of helium to moles using its molar mass (4 g/mol):
n = (15 mg) / (4000 mg/mol) = 0.00375 mol
Then, convert 0°C to Kelvin:
T = 0°C + 273.15 = 273.15 K
Now plug the values into the internal energy formula:
U = (3/2) * 0.00375 mol * 8.314 J/(mol·K) * 273.15 K = 28.89 J
However, the answer choices provided don't include this result, implying that there could be a mistake in the values provided or the units used. Assuming there is a typo in the answer choices and we should select the closest correct answer, (c) 7.5 J seems to be the nearest option, but this doesn't accurately represent the correct computation with the given information.