# Final Temperature Calculator

How to find the final temperature when two objects with different temperatures are mixed? Enter the mass, specific heat, and initial temperature of two objects into the calculator, you can find the final temperature after they are mixed.

### What is the Final Temperature Calculator?

This calculator can determine the final temperature after mixing two things. It uses a rule where the warmer thing loses the same amount of heat that the cooler thing gains. This makes their temperatures even out to a middle number. This tool shows that final number when you put in what the two starting temperatures were.

### How to Use the Calculator

#### Basic Calculator

**Mass of Object 1 (g)**: Enter the mass of the first object (e.g.,`200`

grams).**Specific Heat of Object 1 (J/g°C)**: Input the specific heat capacity of the first object (e.g.,`4.18`

J/g°C).**Initial Temperature of Object 1 (°C)**: Enter the initial temperature of the first object (e.g.,`80`

°C).**Mass of Object 2 (g)**: Enter the mass of the second object (e.g.,`300`

grams).**Specific Heat of Object 2 (J/g°C)**: Input the specific heat capacity of the second object (e.g.,`2.09`

J/g°C).**Initial Temperature of Object 2 (°C)**: Enter the initial temperature of the second object (e.g.,`20`

°C).**Final Temperature (°C)**: This field will display the calculated final temperature after you click the calculate button.

#### Advanced Calculator

**Total Heat Energy Added (J)**: Enter the total heat energy added to the system (e.g.,`5000`

Joules).**Combined Mass of Objects (g)**: Input the combined mass of both objects (e.g.,`500`

grams).**Average Specific Heat of Objects (J/g°C)**: Enter the average specific heat capacity of both objects (e.g.,`3.00`

J/g°C).**Initial Average Temperature of Objects (°C)**: Enter the initial average temperature of both objects (e.g.,`30`

°C).**Final Temperature After Heat Addition (°C)**: This field will display the calculated final temperature after heat addition.

### Formula

For the basic calculator, the formula used is:

${q}_{1}={q}_{2}$

where:

${q}_{1}={m}_{1}\cdot {c}_{1}\cdot ({T}_{f}-{T}_{i1})$

${q}_{2}={m}_{2}\cdot {c}_{2}\cdot ({T}_{f}-{T}_{i2})$

Rearranging for ${T}_{f}$:

${T}_{f}=\frac{({m}_{1}\cdot {c}_{1}\cdot {T}_{i1})+({m}_{2}\cdot {c}_{2}\cdot {T}_{i2})}{({m}_{1}\cdot {c}_{1})+({m}_{2}\cdot {c}_{2})}$

**Variables**

Variable | Description |
---|---|

${m}_{1}$ | Mass of Object 1 (g) |

${c}_{1}$ | Specific Heat of Object 1 (J/g°C) |

${T}_{i1}$ | Initial Temperature of Object 1 (°C) |

${m}_{2}$ | Mass of Object 2 (g) |

${c}_{2}$ | Specific Heat of Object 2 (J/g°C) |

${T}_{i2}$ | Initial Temperature of Object 2 (°C) |

${T}_{f}$ | Final Temperature (°C) |

## How To Calculate Final Temperature

### Example 1: Basic Calculator

**Mass of Object 1 (g)**: 250 grams**Specific Heat of Object 1 (J/g°C)**: 4.18 J/g°C**Initial Temperature of Object 1 (°C)**: 75 °C**Mass of Object 2 (g)**: 350 grams**Specific Heat of Object 2 (J/g°C)**: 2.09 J/g°C**Initial Temperature of Object 2 (°C)**: 25 °C

To calculate the **Final Temperature (°C)**:

1. Calculate the heat content of each object:

${q}_{1}=250\times 4.18\times ({T}_{f}-75)$

${q}_{2}=350\times 2.09\times ({T}_{f}-25)$

2. Set ${q}_{1}={q}_{2}$

`$250\times 4.18\times ({T}_{f}-75)=350\times 2.09\times ({T}_{f}-25)$`

3. Solve for ${T}_{f}$:

$1045({T}_{f}-75)=731.5({T}_{f}-25)$

$1045{T}_{f}-78375=731.5{T}_{f}-18287.5$

$313.5{T}_{f}=60087.5$

${T}_{f}=\frac{60087.5}{313.5}$

${T}_{f}\approx 191.7\text{\hspace{0.17em}}\text{\xb0C}$

So, the final temperature is approximately **191.7 °C**.

#### Example 2: Advanced Calculator

**Total Heat Energy Added (J)**: 8000 Joules**Combined Mass of Objects (g)**: 600 grams**Average Specific Heat of Objects (J/g°C)**: 3.5 J/g°C**Initial Average Temperature of Objects (°C)**: 25 °C

To calculate the **Final Temperature After Heat Addition (°C)**:

1. Use the formula for the final temperature:

`${T}_{f}={T}_{i}+\frac{Q}{m\cdot c}$`

2. Plug in the values:

`${T}_{f}=25+\frac{8000}{600\times 3.5}$`

3. Calculate:

${T}_{f}=25+\frac{8000}{2100}$

${T}_{f}=25+3.81$

${T}_{f}\approx 28.81\text{\hspace{0.17em}}\text{\xb0C}$

So, the final temperature after heat addition is approximately **28.81 °C**.

Thank you for using our tool.