A 100 cm³ box contains helium at a pressure of 2.0 atm and a temperature of 100℃. It is placed in thermal contact with a 200 cm³ box containing argon at a pressure of 4.0 atm and a temperature of 400℃.
b. What is the final thermal energy of each gas?
Verified step by step guidance
1
First, convert the temperatures from Celsius to Kelvin by adding 273.15 to each temperature. This is necessary because the calculations in thermodynamics require absolute temperature in Kelvin.
Use the ideal gas law, PV = nRT, to find the number of moles (n) of each gas. Here, P is the pressure, V is the volume, R is the ideal gas constant (0.0821 L·atm/mol·K), and T is the temperature in Kelvin.
Calculate the initial internal energy of each gas using the formula U = (f/2) nRT, where f is the degrees of freedom of the gas molecules. For helium (a monatomic gas), f = 3, and for argon (also a monatomic gas), f = 3.
Assuming the boxes are thermally insulated from the environment but not from each other, allow the gases to reach thermal equilibrium. The final temperature of both gases can be found by setting the heat lost by one gas equal to the heat gained by the other, and solving for the final temperature.
Calculate the final internal energy of each gas using the same formula U = (f/2) nRT, substituting the final equilibrium temperature for T in the equation.