Three moles of a ideal gas at 200K and 2.0 atm pressure undergo reversible adiabatic compression until the temperature becomes 250 K for the gas `C_(v)" is "27.5JK^(-1)mol^(-1)` in this temperature range. Calculate q, w, `DeltaU,DeltaH` and final V and final P.

Explanation

To solve the problem step by step, we will calculate \( q \), \( w \), \( \Delta U \), \( \Delta H \), final volume \( V \), and final pressure \( P \) for the given adiabatic process involving an ideal gas.

### Given Data:
- Number of moles, \( n = 3 \) moles
- Initial temperature, \( T_1 = 200 \) K
- Final temperature, \( T_2 = 250 \) K
- Initial pressure, \( P_1 = 2.0 \) atm
- Heat capacity at constant volume, \( C_v = 27.5 \) J/(K·mol)
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