I/O Operations Professor Omkar

QUESTION DESCRIPTION 

Omkar is the Professor in SRM he has decided to give a simple task to his students.

He asked his students to create a logic for automatically calculating the amount of energy needed to head X amount of water from Y initial temperature to Z final temperature.

The formula to compute the energy is as follows

Q = M * (finalTemperature – initialTemperature) * 4184

Where,

M is the weight of water in kilograms,

Q is the energy measured in joules,

and

Temperatures are in degree Celsius.

Input Format:

Get the input of amount of water in kilograms , initial temperature of water and final temperature of the water.

Output Format:

Print the energy needed to heat the water.

Refer Sample Testcases

Programming Language need to be used: C++

TEST CASE 1 

INPUT

567 12 56

OUTPUT

The energy needed is 1.04382e+08

TEST CASE 2 

INPUT

734 0 37

OUTPUT

The energy needed is 1.13629e+08

Solution :

#include <iostream>
using namespace std;
int main() {
 int m,f,i,g;
  float q;
  cin>>m;
  cin>>i;
  cin>>f;
  g=(f-i);
  q=m*g*4184;
  cout<<"The energy needed is "<<q;
 return 0;
}

Calculating the Energy to Heat Water: A C++ Program

In this blog, we'll explore a common thermodynamics problem: calculating the energy required to heat water from an initial temperature to a final temperature. This problem is not just an academic exercise—it has practical applications in areas like physics, chemistry, and engineering.

This problem was posed by Omkar, a professor at SRM, who tasked his students with writing a program to automatically compute the energy required to heat water. In this article, we'll break down the problem, explain the necessary formula, and implement a C++ solution step by step. We'll also analyze sample test cases and ensure that our solution is robust and efficient.

Table of Contents

1. Introduction to the Energy Calculation Problem
2. Problem Description and Requirements
3. Understanding the Energy Calculation Formula
4. Approach and Plan for the Solution
5. C++ Code Implementation
6. Explanation of the Code
7. Sample Test Cases and Detailed Analysis
8. Conclusion

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1. Introduction to the Energy Calculation Problem

In many scenarios, calculating the amount of energy required to heat water is a fundamental task. Whether you're heating water for an experiment or calculating energy consumption for a system, the principles remain the same. In this problem, you are tasked with calculating the energy in joules needed to raise a given amount of water from one temperature to another.

Given:

• M: The amount of water in kilograms.
• Initial temperature: The starting temperature of the water.
• Final temperature: The desired temperature after heating.

The formula for calculating the energy is derived from basic thermodynamics.

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2. Problem Description and Requirements

The problem requires us to write a program that:

1. Takes the input of three values:

   • M: The mass of water in kilograms.
   • Initial temperature (Y): The initial temperature of the water in degrees Celsius.
   • Final temperature (Z): The final temperature of the water in degrees Celsius.

2. Computes the energy needed using the formula:

   $$Q = M \times (Z - Y) \times 4184$$

   where:

   • Q: The energy required in joules.
   • M: The mass of water in kilograms.
   • Z: The final temperature in degrees Celsius.
   • Y: The initial temperature in degrees Celsius.

3. Outputs the result in scientific notation with a precision of 5 decimal places.

---

3. Understanding the Energy Calculation Formula

Formula Breakdown:

The formula for calculating the energy needed to heat water is:

$$Q = M \times (Z - Y) \times 4184$$

Where:

• M is the mass of water in kilograms.
• (Z - Y) is the temperature difference between the final temperature and the initial temperature, measured in degrees Celsius.
• 4184 is a constant (specific heat capacity of water) which represents the amount of energy in joules needed to heat 1 kilogram of water by 1 degree Celsius.

The result Q is the amount of energy in joules.

Example:

For example, if you are heating 567 kilograms of water from 12°C to 56°C, the energy required can be calculated using the above formula.

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4. Approach and Plan for the Solution

To solve this problem, we’ll take the following steps:

1. Input: Read the values for the mass of water, the initial temperature, and the final temperature.
2. Calculation: Using the provided formula, calculate the energy required.
3. Output: Display the energy required in joules, formatted to scientific notation with precision.

Step-by-Step Plan:

1. Read the values for:

   • M: Mass of water (in kilograms).
   • Y: Initial temperature (in degrees Celsius).
   • Z: Final temperature (in degrees Celsius).

2. Compute the temperature difference: $\Delta T = Z - Y$.

3. Calculate the energy needed using the formula: $Q = M \times \Delta T \times 4184$.

4. Output the result in a format suitable for scientific notation.

---

5. C++ Code Implementation

Let’s now write the C++ code for the problem:

#include <iostream>
using namespace std;

int main() {
    // Declare variables
    int M, initialTemp, finalTemp;
    float Q;
    
    // Input: Read mass of water, initial and final temperature
    cin >> M >> initialTemp >> finalTemp;
    
    // Calculate the temperature difference
    int tempDifference = finalTemp - initialTemp;
    
    // Calculate the energy needed
    Q = M * tempDifference * 4184;
    
    // Output the result
    cout << "The energy needed is " << Q << endl;
    
    return 0;
}

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6. Explanation of the Code

Key Sections:

1. Input: We take input from the user for the mass of the water (M), the initial temperature (Y), and the final temperature (Z).

   
   cin >> M >> initialTemp >> finalTemp;
   

2. Temperature Difference: We compute the difference between the final temperature and the initial temperature. This gives us the amount by which the water needs to be heated.

   
   int tempDifference = finalTemp - initialTemp;
   

3. Energy Calculation: Using the formula $Q = M \times (Z - Y) \times 4184$, we compute the energy required to heat the water.

   
   Q = M * tempDifference * 4184;
   

4. Output: The result is printed in standard scientific notation. The C++ output stream (cout) will automatically handle large numbers, but if needed, further formatting can be applied to ensure precision.

   
   cout << "The energy needed is " << Q << endl;
   

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7. Sample Test Cases and Detailed Analysis

Test Case 1

Input:

567 12 56

Output:

The energy needed is 1.04382e+08

Explanation:

• Mass of water (M): 567 kg
• Initial temperature (Y): 12°C
• Final temperature (Z): 56°C
• Temperature difference (ΔT): $56 - 12 = 44$
• Energy required (Q): $Q = 567 \times 44 \times 4184 = 1.04382 \times 10^8 \, \text{joules}$

Test Case 2

Input:

734 0 37

Output:

The energy needed is 1.13629e+08

Explanation:

• Mass of water (M): 734 kg
• Initial temperature (Y): 0°C
• Final temperature (Z): 37°C
• Temperature difference (ΔT): $37 - 0 = 37$
• Energy required (Q): $Q = 734 \times 37 \times 4184 = 1.13629 \times 10^8 \, \text{joules}$

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Edge Case:

Input:

0 0 100

Output:

The energy needed is 0

Explanation:

Since there is no water to heat (M = 0), the energy required will be zero, regardless of the temperature change.

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8. Conclusion

The problem of calculating the energy required to heat water is a straightforward application of thermodynamics. We applied the formula for energy in joules and implemented it using basic C++ programming concepts such as input/output handling and arithmetic operations. The provided solution is efficient, easy to understand, and can be applied to a wide variety of scenarios where temperature changes need to be computed.

With this problem solved, you've gained experience in handling scientific calculations in C++ and using appropriate formatting for output in scientific notation. Keep practicing with more such problems to enhance your programming and problem-solving skills!