Change in Internal Energy during Adiabatic Expansion

Given:
- 1 mole of an ideal gas at STP
- Reversible adiabatic expansion to double its volume
- γ (gamma) value is 1.4

To find:
Change in internal energy during the expansion

Solution:

The change in internal energy (∆U) of an ideal gas can be calculated using the equation:

∆U = q - w

Where:
q = heat transfer
w = work done

Since the process is adiabatic, there is no heat transfer (q = 0). Therefore, the equation simplifies to:

∆U = -w

Now, let's calculate the work done during the adiabatic expansion.

Work Done during Adiabatic Expansion:

For an adiabatic process, the work done can be calculated using the equation:

w = -∆E

where ∆E is the change in energy of the gas.

For an ideal gas, the change in energy during an adiabatic process can be expressed as:

∆E = C_v ∆T

Where:
C_v = molar heat capacity at constant volume
∆T = change in temperature

For an adiabatic process, the relationship between pressure and volume can be expressed as:

P₁V₁^γ = P₂V₂^γ

Where:
P₁ = initial pressure
V₁ = initial volume
P₂ = final pressure
V₂ = final volume
γ = heat capacity ratio (specific heat capacity at constant pressure / specific heat capacity at constant volume)

Since the process is reversible and the initial and final states are given, we can use the ideal gas law to find the final pressure:

P₁V₁ = nRT

Where:
n = number of moles
R = ideal gas constant
T = temperature (at STP, temperature is 273 K)

The final volume (V₂) is given as double the initial volume (V₁).

Once we have the initial and final pressures and volumes, we can calculate the change in temperature (∆T) using the adiabatic equation:

∆T = T₂ - T₁ = (P₂V₂ - P₁V₁) / (nR)

Finally, we can substitute the values of ∆T and C_v into the equation for ∆E to find the work done (w), which is equal to -∆E.

Using the calculated value of work done, we can find the change in internal energy (∆U) using the equation ∆U = -w.

Therefore, the correct option is (C) 1373 J.