Let's break down the given problem step by step: **Problem Restatement:** > In a Rankine cycle, steam expands from 3 MPa and 400°C to 10 kPa. What is the turbine work per kg if \( h_1 = 3214 \) kJ/kg and \( h_2 = 2200 \) kJ/kg? Options: - 1000 kJ/kg - 1114 kJ/kg - 714 kJ/kg - 1344 kJ/kg --- ### **Step 1: Understanding the Rankine Cycle** In a Rankine cycle, the turbine work per kg (\( w_t \)) is the difference in enthalpy between the inlet and exit of the turbine: \[ w_t = h_1 - h_2 \] Where: - \( h_1 \) = Enthalpy at turbine inlet (kJ/kg) - \( h_2 \) = Enthalpy at turbine exit (kJ/kg) --- ### **Step 2: Substitute the Given Values** Given: - \( h_1 = 3214 \) kJ/kg - \( h_2 = 2200 \) kJ/kg \[ w_t = 3214 - 2200 \] --- ### **Step 3: Calculate the Turbine Work** \[ w_t = 3214~\text{kJ/kg} - 2200~\text{kJ/kg} \] \[ w_t = 1014~\text{kJ/kg} \] --- ### **Step 4: Match with the Options** The closest value to 1014 kJ/kg from the options is **1000 kJ/kg**. --- ### **Final Answer:** \[ \boxed{1000~\text{kJ/kg}} \] **Explanation:** The turbine work per kg in a Rankine cycle is simply the enthalpy drop across the turbine, \( h_1 - h_2 \). Given values lead directly to 1014 kJ/kg, best matching the option 1000 kJ/kg.

Certainly! Let's go through the problem step-by-step with detailed calculations and explanations. --- ### **Problem Restatement:** In a Rankine cycle, steam expands from a pressure of **3 MPa and 400°C** to **10 kPa**. Given: - Enthalpy at turbine inlet, \( h_1 = 3214 \text{ kJ/kg} \) - Enthalpy at turbine exit, \( h_2 = 2200 \text{ kJ/kg} \) **Question:** Calculate the turbine work per kg of steam, i.e., \( w_{t} = h_1 - h_2 \). --- ### **Step 1: Understand what is being asked** The turbine work per unit mass in a Rankine cycle is given by the difference in enthalpy between the inlet and outlet of the turbine: \[ w_{t} = h_1 - h_2 \] --- ### **Step 2: Plug in the known values** \[ w_{t} = 3214 \text{ kJ/kg} - 2200 \text{ kJ/kg} \] --- ### **Step 3: Perform the subtraction** \[ w_{t} = 3214 - 2200 = 1014 \text{ kJ/kg} \] --- ### **Step 4: Match with options** Given options: - 1000 kJ/kg - 1114 kJ/kg - 714 kJ/kg - 1344 kJ/kg The calculated value, **1014 kJ/kg**, is very close to **1000 kJ/kg**. In practical engineering problems, slight differences can occur due to rounding or approximation; hence, **1000 kJ/kg** is the best match. --- ### **Final Answer:** \[ \boxed{\textbf{1000 kJ/kg}} \] --- ### **Summary:** - The enthalpy drop across the turbine determines the work output. - Calculated \( w_{t} = 1014 \text{ kJ/kg} \), approximate to 1000 kJ/kg. - Therefore, **the turbine work per kg of steam is approximately 1000 kJ**. --- If you have any further questions, feel free to ask!