— Physical Chemistry — Thermodynamics Chemistry Question
Thermodynamics of an Ideal Gas Expansion and Cyclic Refrigeration Process
When an ideal, monatomic gas expands reversibly from a volume V1 to a volume V2, a work
is performed on the system by the surroundings. In this equation, w is the work and p is the pressure of the gas.
Determine the performed work when one mole ideal gas expands isothermally from V1 = 1.00 dm3 to V2 = 20.0 dm3 at the temperature T = 300.0 K.
Given: The gas constant R = 8.314 J K-1 mol-1.
Model Answer
Work performed on the gas is
= –8,314 J K-1 mol-1 × 300 K × ln(20.00 / 1.00) = – 7472 J mol-1 = – 7.47 kJ mol-1
Determine how much heat must be added to the gas during the process given under 7.1.
Model Answer
Because this is an isothermal expansion of an ideal monatomic gas, there is no change in internal energy. From the first law of thermodynamics, we then have that
∆U = q + w = 0
where q is the amount of supplied heat and w is performed work. This leads to
q = –w = 7.47 kJ mol-1.
The gas will perform less work in an adiabatic expansion than in an isothermal expansion. Is this because the adiabatic expansion is characterized by (check the square you think is most important).
1 The volume of the gas is constant
2 The expansion is always irreversible
3 No heat is supplied to the gas
Model Answer
(3) No heat is supplied to the gas.
The cyclic process shown schematically in Figure 1 shows the four steps in a refrigeration system with an ideal gas as working medium. Identify the isothermal and adiabatic steps in the process. Here, TH and TC represent high and low temperature, respectively. Specify for each step whether it is adiabatic or isothermal.
Model Answer
isotherm 1-2 2-3 3-4 4-1
adiabat 1-2 2-3 3-4 4-1