If \(40.0 \mathrm{~kJ}\) of energy are absorbed by \(500.0 \mathrm{~g}\) of water at \(10.0^{\circ} \mathrm{C}\), what is the final temperature of the water?

Short Answer

Expert verified
The final temperature of the water is approximately 29.14°C.

Step by step solution

01

- Understand the formula needed

To solve this problem, use the specific heat formula: \[ q = mc\triangle T \]where:-\(q\) is the heat absorbed (in joules), -\(m\) is the mass (in grams), -\(c\) is the specific heat capacity of water (\(4.18 \text{ J/g°C} \)), -\( \triangle T\) is the change in temperature.
02

- Convert energy units if necessary

Convert the energy from kilojoules (kJ) to joules (J). Since \[ 1 \text{ kJ} = 1000 \text{ J}, \] therefore \[ 40.0 \text{ kJ} = 40.0 \times 1000 = 40000 \text{ J} \].
03

- Rearrange the formula to solve for the final temperature

Rearrange the specific heat formula to solve for \( \triangle T\):\[ \triangle T = \frac{q}{mc} \]. Since \( \triangle T = T_{\text{final}} - T_{\text{initial}}, \) rearrange this to \[ T_{\text{final}} = T_{\text{initial}} + \frac{q}{mc} \].
04

- Plug in the values

Substitute the known values into the equation: \[ T_{\text{final}} = 10.0 + \frac{40000}{500.0 \times 4.18} \].
05

- Calculate the final temperature

Perform the calculation: \[ T_{\text{final}} = 10.0 + \frac{40000}{2090} = 10.0 + 19.14 = 29.14^{\text{C}}. \]

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with Vaia!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

heat absorption
When we talk about heat absorption, we refer to the process where an object takes in heat energy from its surroundings. In this example, the water absorbs heat from an external source. Heat absorption causes the water to gain energy, which can lead to a rise in temperature. This process is essential in many natural phenomena and human activities, such as heating food, boiling water, and even photosynthesis in plants.
To quantify heat absorption, we use the formula
\[ q = mc\triangle T \]
Here, q represents the heat absorbed in joules (J), m is the mass of the substance in grams (g), c is the specific heat capacity (J/g°C), and \( \triangle T \) is the change in temperature (°C).
Understanding the components of this formula is the first step toward grasping how heat absorption works.
energy conversion
Energy conversion is the process of changing energy from one form to another. In our specific heat capacity problem, energy is converted from kilojoules (kJ) to joules (J) because the formula for specific heat requires energy in joules. Converting 40.0 kJ to joules involves a simple multiplication:
  • 1 kJ = 1000 J
  • 40.0 kJ = 40.0 × 1000 = 40000 J

Understanding energy conversion is crucial because it ensures consistency in the units used in calculations. If units are not properly converted, the results may be incorrect.
temperature change
Temperature change is a critical outcome of heat absorption and energy conversion. When an object, like water, absorbs heat, its temperature rises. The formula \(\triangle T = \frac{q}{mc}\) helps us determine this temperature change. In the given problem, water initially at 10.0°C absorbs 40000 J, and its mass is 500.0 g. The specific heat capacity of water is 4.18 J/g°C.
By plugging these values into the formula, we get:
\[ \triangle T = \frac{40000}{500.0 \times 4.18} = 19.14^{\text{C}} \]
This result tells us the increase in temperature. To find the final temperature, add the initial temperature to this change:
\[ T_{\text{final}} = T_{\text{initial}} + \triangle T = 10.0 + 19.14 = 29.14^{\text{C}} \]
The final temperature of the water is 29.14°C, showing how energy absorption leads to a measurable temperature change.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

What happens to the kinetic energy of a speeding car when the car is braked to a stop?

State whether each of the following represents a chemical change or a physical change: (a) A steak is cooked on a grill until well done. (b) In the lab, students firepolish the end of a glass rod. The jagged edge of the glass becomes smooth. (c) Chlorine bleach is used to remove a coffee stain on a white lab coat. (d) When two clear and colorless aqueous salt solutions are mixed together, the solution turns cloudy and yellow. (e) One gram of an orange crystalline solid is heated in a test tube, producing a green powdery solid whose volume is 10 times the volume of the original substance. (f) In the lab, a student cuts a 20 -cm strip of magnesium metal into \(1-\mathrm{cm}\) pieces.

Identify the reactants and products for the electrolysis of water.

Gloves are often worn to protect the hands from being burned when they come in contact with very hot or very cold objects. Gloves are often made of cotton or wool, but many of the newer heat-resistant gloves are made of silicon rubber. The specific heats of these materials are listed below: $$ \begin{array}{|l|c|} \hline \text { Material } & \text { Specific heat }\left(\mathbf{J} / \mathrm{g}^{\circ} \mathbf{C}\right) \\ \hline \text { wool felt } & 1.38 \\ \hline \text { cotton } & 1.33 \\ \hline \text { paper } & 1.33 \\ \hline \text { rubber } & 3.65 \\ \hline \text { silicon rubber } & 1.46 \\ \hline \end{array} $$ (a) If a glove with a mass of \(99.3\) grams composed of cotton increases in temperature by \(15.3^{\circ} \mathrm{F}\), how much energy was absorbed by the glove? (b) A glove with a mass of \(86.2\) grams increases in temperature by \(25.9^{\circ} \mathrm{F}\) when it absorbs \(1.71 \mathrm{~kJ}\) of energy. Calculate the specific heat of the glove and predict its composition. (c) If a glove with a mass of \(50.0\) grams needs to absorb \(1.65 \mathrm{~kJ}\) of energy, how much will the temperature of the glove increase for each of the materials listed above? (d) Which is the best material for a heat-resistant glove? (e) If you were designing a heat-resistant glove, what kind of specific heat would you look for?

A 275 -g sample of a metal requires \(10.75 \mathrm{~kJ}\) to change its temperature from \(21.2^{\circ} \mathrm{C}\) to its melting temperature, \(327.5^{\circ} \mathrm{C}\). What is the specific heat of this metal?

See all solutions

Recommended explanations on Chemistry Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free