The 50 MWe Andasol solar thermal power plant in Spain uses two tanks of molten salt (specific heat c= 1.47 kJ/kg °C), each storing 28,000 tonne. The salt is heated from 293°C to 550°C. How much energy is stored in each tank? В. A. If the efficiency is 16%, how long can the plant operate to produce 50 MW.?

College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
icon
Related questions
Question

Picture of question attached. Thanks for the help!

**Problem 9.8**

The 50 MW\(_e\) Andasol solar thermal power plant in Spain uses two tanks of molten salt (specific heat \( c = 1.47 \text{ kJ/kg} \cdot °C \)), each storing 28,000 tonnes. The salt is heated from 293°C to 550°C.

**A. How much energy is stored in each tank?**
**B. If the efficiency is 16%, how long can the plant operate to produce 50 MW?**

---

### Detailed Analysis

**A. Calculating Energy Stored in Each Tank**

To find the total energy stored in each tank, we use the formula for heat energy:

\[ Q = mc\Delta T \]

where:
- \( Q \) is the heat energy stored (in kJ),
- \( m \) is the mass of the molten salt (in kg),
- \( c \) is the specific heat capacity (in kJ/kg°C),
- \( \Delta T \) is the change in temperature (in °C).

Given:
- Mass \( m \) = 28,000 tonnes = 28,000,000 kg
- Specific heat capacity \( c \) = 1.47 kJ/kg°C
- Temperature change \( \Delta T \) = 550°C - 293°C = 257°C

Substitute the values into the formula:

\[ Q = 28,000,000 \, \text{kg} \times 1.47 \, \text{kJ/kg} \cdot °C \times 257 \, °C \]
\[ Q = 10,580,400,000 \, \text{kJ} \]

So, the energy stored in each tank is 10,580,400,000 kJ.

**B. Operating Time to Produce 50 MW**

To produce 50 MW with an efficiency of 16%, we need to find the useful energy produced by each tank and then determine how long the tank can produce electricity.

First, calculate the useful energy (in kJ) that can be extracted at 16% efficiency:

\[ \text{Useful Energy} = Q \times \text{Efficiency} \]
\[ \text{Useful Energy} = 10,580,400,000 \, \text{kJ} \times 0.16 \]
\[ \text{Useful Energy} =
Transcribed Image Text:**Problem 9.8** The 50 MW\(_e\) Andasol solar thermal power plant in Spain uses two tanks of molten salt (specific heat \( c = 1.47 \text{ kJ/kg} \cdot °C \)), each storing 28,000 tonnes. The salt is heated from 293°C to 550°C. **A. How much energy is stored in each tank?** **B. If the efficiency is 16%, how long can the plant operate to produce 50 MW?** --- ### Detailed Analysis **A. Calculating Energy Stored in Each Tank** To find the total energy stored in each tank, we use the formula for heat energy: \[ Q = mc\Delta T \] where: - \( Q \) is the heat energy stored (in kJ), - \( m \) is the mass of the molten salt (in kg), - \( c \) is the specific heat capacity (in kJ/kg°C), - \( \Delta T \) is the change in temperature (in °C). Given: - Mass \( m \) = 28,000 tonnes = 28,000,000 kg - Specific heat capacity \( c \) = 1.47 kJ/kg°C - Temperature change \( \Delta T \) = 550°C - 293°C = 257°C Substitute the values into the formula: \[ Q = 28,000,000 \, \text{kg} \times 1.47 \, \text{kJ/kg} \cdot °C \times 257 \, °C \] \[ Q = 10,580,400,000 \, \text{kJ} \] So, the energy stored in each tank is 10,580,400,000 kJ. **B. Operating Time to Produce 50 MW** To produce 50 MW with an efficiency of 16%, we need to find the useful energy produced by each tank and then determine how long the tank can produce electricity. First, calculate the useful energy (in kJ) that can be extracted at 16% efficiency: \[ \text{Useful Energy} = Q \times \text{Efficiency} \] \[ \text{Useful Energy} = 10,580,400,000 \, \text{kJ} \times 0.16 \] \[ \text{Useful Energy} =
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps

Blurred answer
Knowledge Booster
Unit conversion
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.
Recommended textbooks for you
College Physics
College Physics
Physics
ISBN:
9781305952300
Author:
Raymond A. Serway, Chris Vuille
Publisher:
Cengage Learning
University Physics (14th Edition)
University Physics (14th Edition)
Physics
ISBN:
9780133969290
Author:
Hugh D. Young, Roger A. Freedman
Publisher:
PEARSON
Introduction To Quantum Mechanics
Introduction To Quantum Mechanics
Physics
ISBN:
9781107189638
Author:
Griffiths, David J., Schroeter, Darrell F.
Publisher:
Cambridge University Press
Physics for Scientists and Engineers
Physics for Scientists and Engineers
Physics
ISBN:
9781337553278
Author:
Raymond A. Serway, John W. Jewett
Publisher:
Cengage Learning
Lecture- Tutorials for Introductory Astronomy
Lecture- Tutorials for Introductory Astronomy
Physics
ISBN:
9780321820464
Author:
Edward E. Prather, Tim P. Slater, Jeff P. Adams, Gina Brissenden
Publisher:
Addison-Wesley
College Physics: A Strategic Approach (4th Editio…
College Physics: A Strategic Approach (4th Editio…
Physics
ISBN:
9780134609034
Author:
Randall D. Knight (Professor Emeritus), Brian Jones, Stuart Field
Publisher:
PEARSON