A motor draws some gas from an adiabatic container of volume 2 liters having a monoatomic gas at a pressure 4 atm. After drawing the gas the pressure in the container reduces to 1 atm. If the motor converts `10%` of the energy contained in the drawn gas and the output of the motor is 10 p joule, then find the value of p.use `(1atm=10^(5)` pascal)

Explanation

To solve the problem, we will follow these steps:

### Step 1: Understand the problem
We have an adiabatic container with a monoatomic gas. The initial pressure is 4 atm, and after some gas is drawn, the pressure drops to 1 atm. We need to find the value of \( p \) given that the motor converts 10% of the energy contained in the drawn gas into output energy of \( 10p \) joules.

### Step 2: Calculate the work done by the gas
Since the container is adiabatic, the work done by the gas can be calculated using the pressures and the volume of the gas.

1. **Initial Pressure (P_initial)** = 4 atm
2. **Final Pressure (P_final)** = 1 atm
3. **Volume (V)** = 2 liters = \( 2 \times 10^{-3} \) m³ (since 1 liter = \( 10^{-3} \) m³)
4. **Convert pressures to Pascals**:
- \( P_{initial} = 4 \, \text{atm} \times 10^5 \, \text{Pa} = 4 \times 10^5 \, \text{Pa} \)
- \( P_{final} = 1 \, \text{atm} \times 10^5 \, \text{Pa} = 1 \times 10^5 \, \text{Pa} \)

5. **Work done by the gas (W)** can be calculated using the formula:
\[ W = P_{initial} \cdot V - P_{final} \cdot V \]
\[ W = (4 \times 10^5 \, \text{Pa} - 1 \times 10^5 \, \text{Pa}) \cdot (2 \times 10^{-3} \, \text{m}^3) \]
\[ W = (3 \times 10^5 \, \text{Pa}) \cdot (2 \times 10^{-3} \, \text{m}^3) = 600 \, \text{J} \]

### Step 3: Calculate the energy converted by the motor
The motor converts 10% of the work done into output energy:
\[ \text{Output Energy} = 0.1 \cdot W = 0.1 \cdot 600 \, \text{J} = 60 \, \text{J} \]

### Step 4: Relate the output energy to \( p \)
According to the problem, the output of the motor is given as \( 10p \) joules:
\[ 10p = 60 \, \text{J} \]

### Step 5: Solve for \( p \)
\[ p = \frac{60}{10} = 6 \]

### Final Answer
The value of \( p \) is \( 6 \).

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