Three moles on an ideal gas at 300 K are isothermally expanded to five times its volume and heated at this constant volume so that the pressure is raised to its initial value before expansion. In the whole process 83.14 kJ heat is required Calculate the ratio `((C_P)/(C_V))` of the gas `[log_e5=1.61]`

Explanation

To solve the problem step by step, we will analyze the process of the ideal gas and calculate the required ratio \( \frac{C_P}{C_V} \).

### Step 1: Understand the Process
The gas undergoes two main processes:
1. Isothermal expansion from initial state (P0, V0, T0) to (P2, 5V0, T0).
2. Isochoric (constant volume) heating from (P2, 5V0, T0) to (P0, 5V0, T3).

### Step 2: Initial Conditions
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