Two moles of an idela gas at `2atm` and `27^(@)C` is compressed isothermally to one-half of its volume by an external pressure of `4atm`. Calculate `q,w`, and `DeltaU`.

Explanation

To solve the problem, we need to calculate the heat transfer (q), work done (w), and change in internal energy (ΔU) for the isothermal compression of an ideal gas. Here’s a step-by-step solution:

### Step 1: Convert Given Values
We are given:
- Number of moles (n) = 2 moles
- Initial pressure (P₁) = 2 atm
- Initial temperature (T) = 27°C = 300 K (since T(K) = T(°C) + 273)
- External pressure (P_ext) = 4 atm
...