What is the total internal energy of 5.00molmol of 30∘C^\circ C He\rm{He} gas and O2\rm{O_2} gas, respectively?
To calculate the total internal energy of a gas, we need to use the formula:
Internal energy (U) = (3/2) * n * R * T,
where n is the number of moles of the gas, R is the ideal gas constant, and T is the temperature in Kelvin.
First, let's convert the temperature from Celsius to Kelvin. The conversion formula is:
Kelvin = Celsius + 273.15.
For He gas:
- n = 5.00 mol
- T = 30 °C = 30 + 273.15 = 303.15 K
For O2 gas:
- n = 5.00 mol
- T = 30 °C = 30 + 273.15 = 303.15 K
Now, let's substitute the values into the formula for internal energy for both gases.
For He gas:
U_He = (3/2) * 5.00 mol * R * 303.15 K
For O2 gas:
U_O2 = (3/2) * 5.00 mol * R * 303.15 K
To find the total internal energy, we need to sum the internal energies of both gases:
Total Internal energy = U_He + U_O2
Now, we can calculate the total internal energy using the given information.