Answer:
1) V₂ = 0.0266 m³
2) W = 2.26 kJ
3) Q = -2.26 kJ
Explanation:
The ideal gas law says that the pressure (P) times volume (V) equals the number of moles (n) times the ideal gas constant (R) times the temperature (T). In an isothermal process, temperature is constant. For an ideal gas, the work done can be calculated using the final and initial pressures, and the heat transferred is opposite of the work done.
Part 1 of 3
The ideal gas law is PV = nRT. In an isothermal process, temperature is constant. So the final temperature is also the initial temperature.
P₂V₂ = nRT
(0.77 atm) (101325 Pa/atm) V₂ = (2 mol) (8.31451 J/K/mol) (125 K)
V₂ = 0.0266 m³
Part 2 of 3
For an ideal gas in an isothermal process, work can be calculated with:
W = nRT ln(P₁/P₂)
W = (2 mol) (8.31451 J/K/mol) (125 K) ln(0.77 / 0.26)
W = 2260 J
W = 2.26 kJ
Part 3 of 3
For an ideal gas in an isothermal process, there is no change in internal energy, so the heat is equal and opposite of the work.
Q = -W
Q = -2.26 kJ