Thermodynamic Processes of Ideal Gas Expansion: Work, Heat, Internal Energy and Enthalpy Changes

For each process, we can use the ideal gas law and the first law of thermodynamics to calculate the values of W, Q, ΔU, and ΔH.

(1) Free expansion process: In a free expansion process, the gas expands into a vacuum, so no work is done on or by the system. Therefore, W = 0.

Since the process is adiabatic (no heat transfer), Q = 0.

From the first law of thermodynamics, ΔU = Q - W = 0 - 0 = 0.

Since the process is adiabatic, ΔH = ΔU = 0.

(2) Expands against constant external pressure p_su = 100000 Pa: The work done in this process can be calculated using the formula: W = -pΔV, where p is the external pressure and ΔV is the change in volume.

Since the pressure is constant, we can use the ideal gas law to calculate the change in volume: ΔV = V2 - V1 = nRT2/p2 - nRT1/p1

Substituting the given values: ΔV = 10 mol * 8.314 J/(molK) * (25 + 273.15 K) / 100000 Pa - 10 mol * 8.314 J/(molK) * (25 + 273.15 K) / 10000000 Pa

Calculating ΔV: ΔV = 0.025 m^3 - 0.0025 m^3 = 0.0225 m^3

Calculating the work done: W = -pΔV = -100000 Pa * 0.0225 m^3 = -2250 J

Since the process is adiabatic (no heat transfer), Q = 0.

From the first law of thermodynamics, ΔU = Q - W = 0 - (-2250 J) = 2250 J.

Since there is no change in pressure, ΔH = ΔU = 2250 J.

(3) Expands isothermally and reversibly: In an isothermal process, the temperature remains constant. Therefore, ΔU = 0.

From the first law of thermodynamics, Q = W.

Since the process is reversible, we can use the formula for work done in an isothermal process: W = -nRTln(V2/V1)

Substituting the given values: W = -10 mol * 8.314 J/(mol*K) * (25 + 273.15 K) * ln((25 + 273.15 K) / (25 + 273.15 K))

Calculating W: W = 0 J

Since Q = W and no work is done, Q = 0.

Since ΔU = 0 and the process is isothermal, ΔH = 0.

To summarize: (1) Free expansion process: W = 0, Q = 0, ΔU = 0, ΔH = 0. (2) Expands against constant external pressure p_su = 100000 Pa: W = -2250 J, Q = 0, ΔU = 2250 J, ΔH = 2250 J. (3) Expands isothermally and reversibly: W = 0 J, Q = 0, ΔU = 0, ΔH = 0.