ton 8 © s
Oech nt work Gone of A817 ik an compression of The Beg feces 1 TC 01009. For hs ck, cal eve
p : ted j
E. 1 E
E -
Came i
= 3 a

Question

ton 8 © s
Oech nt work Gone of A817 ik an compression of The Beg feces 1 TC 01009. For hs ck, cal eve
p : ted j
E. 1 E
E -
Came i
= 3 a

VIPSolutions · Accepted Answer

Let's solve the problem step-by-step:

**Given:**
- Net work done ($W_{net}$) = 418.17 kJ/kg
- Compression ratio ($r$) = 8
- Beginning of process: $T_1 = 17^\circ C = 290 K$, $P_1 = 100 \text{ kPa}$

**Required:**  
Mean Effective Pressure (MEP)

---

### Step 1: Find the Specific Volume at the Start $v_1$

For air (ideal gas),
$$
P_1 v_1 = R T_1
$$
Where $R = 0.287 \text{ kJ/kg·K}$.

$$
v_1 = \frac{R T_1}{P_1}
$$
$$
v_1 = \frac{0.287 \times 290}{100} = \frac{83.23}{100} = 0.8323 \text{ m}^3/\text{kg}
$$

### Step 2: Find the Displacement Volume per kg

$$
\text{Displacement volume per kg} = v_1 \left(1 - \frac{1}{r}\right)
$$
$$
= 0.8323 \left(1 - \frac{1}{8}\right)
= 0.8323 \times \frac{7}{8}
= 0.728 \text{ m}^3/\text{kg}
$$

### Step 3: Calculate the Mean Effective Pressure (MEP)

$$
\text{MEP} = \frac{W_{net}}{\text{Displacement Volume}}
$$
$$
= \frac{418.17}{0.728}
= 574.4 \text{ kPa}
$$

### Step 4: Match with the Options

The closest answer is **574 kPa**.

---

**Final Answer:**  
$$
\boxed{574 \text{ kPa}}
$$

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ton 8 © s Oech nt work Gone of A817 ik an compression of The Beg feces 1 TC 01009. For hs ck, cal eve p : ted j E. 1 E E - Came i = 3 a

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