Pregunta
upstudy study bank question image url

QUESTION 5 Within 30 minutes, 2 liters of water must be heated from \( 10^{\circ} \mathrm{C} \) to \( 80^{\circ} \mathrm{C} \), The specific heat capacity of water is \( 4,187 \mathrm{~kJ} / \mathrm{kg} \). K . The efficiency of the heating system in \( 68 \% \). 5.1 What is the net amount of energy delivered to the water? 5.2 The voltage supply is 200 V . Determine the value of the current.

Ask by Hobbs Lewis. in South Africa
Mar 18,2025

Solución de inteligencia artificial de Upstudy

Respuesta verificada por el tutor

Responder

5.1 The net energy delivered to the water is approximately 586,180 joules. 5.2 The current required is approximately 2.39 amperes.

Solución

\[ \textbf{5.1 Calculation of the net energy delivered to the water:} \] 1. \(\textbf{Mass of water:}\) Since the density of water is approximately \(1\, \text{kg/L}\), 2 liters of water have a mass of \[ m = 2\, \text{kg}. \] 2. \(\textbf{Temperature change:}\) The water is heated from \(10^{\circ}\text{C}\) to \(80^{\circ}\text{C}\), so the change in temperature is \[ \Delta T = 80^{\circ}\text{C} - 10^{\circ}\text{C} = 70\, \text{K}. \] 3. \(\textbf{Specific heat capacity:}\) The specific heat capacity of water is given as \[ c = 4187\, \frac{\text{J}}{\text{kg}\cdot\text{K}}. \] 4. \(\textbf{Net energy delivered:}\) Using the formula \[ Q = m \cdot c \cdot \Delta T, \] we have \[ Q = 2\, \text{kg} \times 4187\, \frac{\text{J}}{\text{kg}\cdot\text{K}} \times 70\, \text{K} \approx 586180\, \text{J}. \] \[ \textbf{5.2 Determination of the current:} \] 1. \(\textbf{Accounting for system efficiency:}\) The heating system operates at an efficiency of \(68\%\) (\(\eta = 0.68\)). This means that in order to deliver \(Q\) joules of energy to the water, the total energy supplied electrically must be \[ E_{\text{supplied}} = \frac{Q}{\eta} = \frac{586180\, \text{J}}{0.68} \approx 861147\, \text{J}. \] 2. \(\textbf{Time available for heating:}\) The time given is 30 minutes, which in seconds is \[ t = 30\, \text{min} \times 60\, \frac{\text{s}}{\text{min}} = 1800\, \text{s}. \] 3. \(\textbf{Power required:}\) The power \(P\) needed to supply this energy in the given time is \[ P = \frac{E_{\text{supplied}}}{t} \approx \frac{861147\, \text{J}}{1800\, \text{s}} \approx 478.4\, \text{W}. \] 4. \(\textbf{Current calculation from the voltage supply:}\) Given the supply voltage \(V = 200\, \text{V}\), the current \(I\) drawn is given by \[ I = \frac{P}{V} \approx \frac{478.4\, \text{W}}{200\, \text{V}} \approx 2.392\, \text{A}. \] \[ \textbf{Final Answers:} \] \[ \text{5.1 } Q \approx 586180\, \text{J}, \] \[ \text{5.2 } I \approx 2.39\, \text{A}. \]

Respondido por UpStudy AI y revisado por un tutor profesional

error msg
Explicar
Simplifique esta solución

Bonus Knowledge

To find the net amount of energy delivered to the water, first calculate the energy needed to raise the temperature. The formula to compute the heat energy is \( Q = m \cdot c \cdot \Delta T \), where \( m \) is the mass of water (2 liters \(\approx\) 2 kg), \( c \) is the specific heat capacity \( 4,187 \, \text{kJ/kg·K} \), and \( \Delta T \) is the change in temperature (from \( 10^{\circ}C \) to \( 80^{\circ}C \), which is \( 70^{\circ}C \)). Thus, \( Q = 2 \, \text{kg} \cdot 4,187 \, \text{kJ/kg·K} \cdot 70 \, \text{K} = 58618 \, \text{kJ} \) (or \( 58.62 \, \text{MJ} \)). Considering the efficiency of the heating system at \( 68\% \): Net energy delivered = \( \frac{Q}{\text{efficiency}} = \frac{58618 \, \text{kJ}}{0.68} \approx 86106 \, \text{kJ} \). Next, to determine the value of the current, we'll use the power formula. Power \( P = \frac{Q}{t} \), where \( t \) is the time in hours (30 minutes = 0.5 hours). Convert the delivered energy into watts \( (1 \, \text{kW} = 1000 \, \text{J/s}) \): \( P = \frac{86106 \, \text{kJ}}{0.5 \, \text{hr}} = 172212 \, \text{kW} \times 1000 \text{W/kW} = 172212000 \text{W} \). Now use \( P = V \cdot I \) to find I: \( I = \frac{P}{V} = \frac{172212000 \, \text{W}}{200 \, \text{V}} \approx 861060 \, \text{A} \). Now, let’s take a little journey into the world of thermodynamics and electricity! This scenario demonstrates the importance of efficiency in energy systems. If your heating equipment is not working efficiently, you might end up with sky-high energy bills! Oh, and always remember to double-check your calculations; a small mistake could lead to big differences in results. So grab your calculator and make sure you're heating that water just right!

preguntas relacionadas

Latest Physics Questions

DIRECTIONS: READ AND UNDERSTAND TEST QUESTIONS CAREFULLY AND WRITE LETTER OF YOUR ANSWER BEFORE EACH NUMBER. \( \qquad \) 1. What force enables objects to reach the ground? A. Frictional Force B. Magnetic Force \( \qquad \) C. Gravitational Force 2. What is the shape of the trajectory Tension Force A. Circular B. Elliptical \( \qquad \) C. Hyperbolic D. Parabolic 3. Which of the following composed the two linear motions of a projectile? A. Horizontal and Circular Motion B. Vertical and Circular Motion \( \qquad \) C. Horizontal and Vertical Motion D. Vertical and Curvilinear Motion acted solely upon by gravitational force? A. Project B. Projectile \( \qquad \) C. Target 5. What do you call the path followed by an object under projectile motion? A. Project B. Projectile C. Target 6. What D. Trajectory \( \qquad \) 6. What happens to the vertical velocity of an object as it travels through the air? A. Changes continuously C. Gradually increases B. Gradually decreases D. Remains the same \( \qquad \) 7. What happens to the horizontal velocity of an object as it travels through the air? A. Changes continuously C. Gradually increases B. Gradually decreases D. Remains the same \( \qquad \) 8. If you throw a baseball straight up, what is its vertical velocity at the highest point? A. \( 0 \mathrm{~m} / \mathrm{s} \) C. \( 0 \mathrm{~m} / \mathrm{s} 2 \) B. \( 9.8 \mathrm{~m} / \mathrm{s} \) D. \( -9.8 \mathrm{~m} / \mathrm{s} 2 \) 9. If a stone is horizontally launched at a certain height, how do you describe the magnitude of its vertical velocity as it approaches the ground? A. Changes continuously C. Gradually increasing B. Gradually decreasing D. Remains the same
Física Philippines Mar 19, 2025
¡Prueba Premium ahora!
¡Prueba Premium y hazle a Thoth AI preguntas de matemáticas ilimitadas ahora!
Quizas mas tarde Hazte Premium
Estudiar puede ser una verdadera lucha
¿Por qué no estudiarlo en UpStudy?
Seleccione su plan a continuación
Prima

Puedes disfrutar

Empieza ahora
  • Explicaciones paso a paso
  • Tutores expertos en vivo 24/7
  • Número ilimitado de preguntas
  • Sin interrupciones
  • Acceso completo a Respuesta y Solución
  • Acceso completo al chat de PDF, al chat de UpStudy y al chat de navegación
Básico

Totalmente gratis pero limitado

  • Solución limitada
Bienvenido a ¡Estudia ahora!
Inicie sesión para continuar con el recorrido de Thoth AI Chat
Continuar con correo electrónico
O continuar con
Al hacer clic en "Iniciar sesión", acepta nuestros términos y condiciones. Términos de Uso & Política de privacidad