Final answer:
To calculate the change in internal energy (ΔE) for the helium-filled balloon, convert the mass of helium to moles, then use the formula ΔE = nCpΔT with the known values of moles, Cp, and temperature change. The final step is to convert the answer to kJ.
Step-by-step explanation:
The question you've asked involves applying concepts from thermodynamics to calculate the change in internal energy (ΔE) for a helium-filled balloon as it goes through a temperature change while keeping the pressure constant.
To find ΔE, we use the formula ΔE = nCpΔT, where n is the number of moles of the gas, Cp is the molar heat capacity at constant pressure, and ΔT is the change in temperature. Assuming that the given mass of helium (313 g) corresponds to the number of moles in the balloon, we first need to convert grams to moles using helium's molar mass (4.00 g/mol). Once we have the number of moles, we can calculate the change in internal energy.
The change in temperature is given as 15.0°C, so ΔT is -15.0°C (since the temperature decreases). Given that Cp for helium is 20.8 J/°C·mol, we simply perform the calculation:
ΔE = nCpΔT
Substitute the known values:
ΔE = (313 g He / 4.00 g/mol) * 20.8 J/°C mol * (-15.0°C)
Now, we calculate the numerical value and convert it to kJ:
ΔE = -ΔE (in kJ)
This will give us the change in internal energy of the balloon in kJ.