One mole of an ideal gas at 25C and 1 bar is allowed to expand adiabatically against a constant external pressure of 1.00 bar from 1.00 dm^3 to 10.00 dm^3. Calculate the final temperature, q, w, delta_U and delta_H.

To calculate the final temperature, q, w, delta_U, and delta_H for the given adiabatic expansion of an ideal gas, we will need to use the first law of thermodynamics and the adiabatic expansion equation.

Let's break down the steps to find each parameter:

1. Final Temperature (Tf):
The adiabatic expansion equation for an ideal gas is given by:
T1 * V1^(γ-1) = T2 * V2^(γ-1)
Where γ (gamma) is the heat capacity ratio, which is specific to each gas. For an ideal monoatomic gas, γ is equal to 5/3.

Substituting the values:
T1 = 25°C = 298K (given)
V1 = 1.00 dm^3 (given)
V2 = 10.00 dm^3 (given)

Rearranging the equation, we can solve for Tf:
Tf = T1 * (V1/V2)^((γ-1)/γ)

2. Work Done (w):
In an adiabatic process, no heat (q) is exchanged between the system and its surroundings. Hence, q = 0.

The work done can be calculated using the formula:
w = -Pext * (V2 - V1)
Where Pext is the external pressure (given).

Substituting the values:
Pext = 1.00 bar (given)
V1 = 1.00 dm^3 (given)
V2 = 10.00 dm^3 (given)

Calculate w using the formula.

3. Change in Internal Energy (delta_U):
Since this is an adiabatic process, no heat is transferred (q = 0), and the change in internal energy (delta_U) of an ideal gas is given by:
delta_U = w

4. Change in Enthalpy (delta_H):
In an adiabatic process, the change in enthalpy (delta_H) is given by:
delta_H = delta_U + Pext * (V2 - V1)

Substitute the values:
delta_U = w
V1 = 1.00 dm^3 (given)
V2 = 10.00 dm^3 (given)
Pext = 1.00 bar (given)

Now, you can use these steps and the provided formulas to calculate the final temperature (Tf), work done (w), change in internal energy (delta_U), and change in enthalpy (delta_H) for the given adiabatic expansion of the ideal gas.