## Related questions with answers

Water at 70 kPa and $100^\circ C$ is compressed isentropically in a closed system to 4 MPa. Determine the final temperature of the water and the work required, in kJ/kg, for this compression.

Solutions

Verified$\textbf{Required}$

Determine the final temperature of water and the work required for this compression.

To solve this problem, we take the contents of the cylinders as the system. This is a closed system, since no mass enter or leaves it. The energy balance for this stationary closed system can be expressed as it follows:

$\begin{aligned} \Delta E_{\text{system}} &=& E_{\text{in}} - E_{text{out}}\\ \Delta u &=& (u_2 - u_1) = w_{\text{in}} \end{aligned}$

Therefore we need the values of the internal energy in the initial and in the final state. These can be found in Table A-6:

$\begin{equation*} \left.\begin{array}{l} P_{1}=70 \mathrm{kPa} \\ T_{1}=100^{\circ} \mathrm{C} \end{array}\right\} \quad \begin{array}{l} u_{1}=2509.4 \mathrm{~kJ} / \mathrm{kg} \\ s_{1}=7.5344 \mathrm{~kJ} / \mathrm{kg} \cdot \mathrm{K} \end{array} \end{equation*}$

The process is isentropic, which means that the entropy remains constant during the process. The properties at the final state are:

$\begin{equation*} \left.\begin{array}{l} P_{2}=4 \mathrm{MPa} \\ s_{2}=s_{1}=7.5344 \mathrm{~kJ} / \mathrm{kg} \cdot \mathrm{K} \end{array}\right\} \quad \begin{array}{l} u_{2}=3396.5 \mathrm{~kJ} / \mathrm{kg} \\ T_{2}=664^{\circ} \mathrm{C} \end{array} \end{equation*}$

Therefore the work done during this compression process is:

$\begin{aligned} w_{\mathrm{in}} &=& u_{2}-u_{1}\\ &=& (3396.5-2509.4) \mathrm{kJ} / \mathrm{kg}\\ &=& \boxed{887.1 \:\frac{\mathrm{kJ}}{\mathrm{kg}}} \end{aligned}$

## Create an account to view solutions

## Create an account to view solutions

## Recommended textbook solutions

#### Fundamentals of Thermal-Fluid Sciences

5th Edition•ISBN: 9780078027680 (5 more)John Cimbala, Robert Turner, Yunus A. Cengel#### Fundamentals of Electric Circuits

6th Edition•ISBN: 9780078028229 (12 more)Charles Alexander, Matthew Sadiku#### Physics for Scientists and Engineers: A Strategic Approach with Modern Physics

4th Edition•ISBN: 9780133942651 (4 more)Randall D. Knight## More related questions

1/4

1/7