Calculate Heat Required Iron Cube Temperature Change

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In the realm of thermodynamics, understanding the concept of heat transfer is paramount. Heat, a form of energy, is the driving force behind temperature changes in matter. When heat is added to a substance, its particles move faster, resulting in an increase in temperature. The amount of heat required to produce a specific temperature change depends on several factors, including the mass of the substance, its specific heat capacity, and the magnitude of the temperature change. In this comprehensive article, we will delve into the fascinating world of heat transfer, focusing on a practical example: calculating the amount of heat required to raise the temperature of an iron cube. We will explore the fundamental concepts underlying this calculation, including specific heat capacity, and walk through the step-by-step process of applying the relevant formula. By the end of this exploration, you will have a firm grasp of how to quantify heat transfer and its relationship to temperature changes.

Before we embark on the calculation, it is essential to establish a solid understanding of the key concepts involved. These concepts form the bedrock of our analysis and will guide us through the process. Let's begin by defining heat itself. In thermodynamics, heat is the energy transferred between objects or systems due to a temperature difference. It is not a property of the object itself, but rather a process of energy transfer. Heat always flows from a region of higher temperature to a region of lower temperature, striving to establish thermal equilibrium. This transfer of energy manifests as changes in the kinetic energy of the particles within the substance. Next, we encounter the concept of specific heat capacity. Specific heat capacity, often denoted as Cp, is an intrinsic property of a substance that dictates the amount of heat required to raise the temperature of one gram of that substance by one degree Celsius (or one Kelvin). It is a measure of a substance's resistance to temperature change. Substances with high specific heat capacities require more heat to undergo a temperature change compared to substances with low specific heat capacities. For instance, water has a remarkably high specific heat capacity, which is why it is an excellent coolant and plays a crucial role in regulating Earth's climate. Understanding specific heat capacity is crucial for accurately calculating heat transfer. Finally, the formula that governs heat transfer in scenarios involving temperature changes without phase transitions is:

Q=mcâ–³TQ = mc \triangle T

Where:

  • Q represents the amount of heat transferred (in joules)
  • m is the mass of the substance (in grams)
  • Cp denotes the specific heat capacity of the substance (in J/g·°C)
  • ΔT symbolizes the change in temperature (in °C), calculated as the final temperature (Tfinal) minus the initial temperature (Tinitial)

This formula is the cornerstone of our calculation and provides a direct relationship between heat transfer, mass, specific heat capacity, and temperature change. With these concepts in place, we are well-prepared to tackle the problem at hand.

Now, let's state the specific problem we aim to solve. We have a cube of iron, a common metal with a specific heat capacity (Cp) of 0.450 J/g·°C. The cube has a mass of 55.8 grams. Initially, the iron cube is at a temperature of 25.0°C. We want to heat this cube until it reaches a final temperature of 49.0°C. Our objective is to determine the amount of heat, in joules, that is required to raise the temperature of the iron cube from its initial temperature to its final temperature. This is a classic heat transfer problem that allows us to apply the formula we discussed earlier and solidify our understanding of the concepts involved. To solve this problem effectively, we will follow a systematic approach, carefully identifying the given values, applying the formula, and performing the necessary calculations. This step-by-step approach will not only lead us to the correct answer but also reinforce our problem-solving skills in thermodynamics.

To solve this problem systematically, we'll follow a step-by-step approach that ensures accuracy and clarity. This approach will not only lead us to the correct answer but also reinforce our problem-solving skills in thermodynamics.

Step 1: Identify the Given Values

The first step in any problem-solving endeavor is to carefully identify the given values. This sets the stage for applying the correct formulas and calculations. In our problem, we are provided with the following information:

  • Mass of the iron cube (m): 55.8 g
  • Specific heat capacity of iron (Cp): 0.450 J/g·°C
  • Initial temperature (Tinitial): 25.0°C
  • Final temperature (Tfinal): 49.0°C

These values are the building blocks of our solution, and we will use them in the subsequent steps to calculate the heat required.

Step 2: Calculate the Temperature Change

The next step is to determine the temperature change (ΔT), which represents the difference between the final and initial temperatures. This value is crucial for quantifying the thermal process. We calculate ΔT using the following formula:

△T=Tfinal−Tinitial \triangle T = T_{final} - T_{initial}

Substituting the given values, we get:

△T=49.0°C−25.0°C=24.0°C \triangle T = 49.0 \degree C - 25.0 \degree C = 24.0 \degree C

Therefore, the temperature change is 24.0°C. This positive value indicates that the temperature of the iron cube increased during the heating process.

Step 3: Apply the Heat Transfer Formula

Now that we have all the necessary components, we can apply the heat transfer formula to calculate the amount of heat (Q) required. The formula, as we discussed earlier, is:

Q=mcâ–³T Q = mc \triangle T

We will now substitute the values we identified in Step 1 and calculated in Step 2 into this formula. This will allow us to determine the amount of heat required to raise the temperature of the iron cube.

Step 4: Substitute the Values and Calculate

With the formula in hand, we can now substitute the values we have gathered: the mass of the iron cube (m), the specific heat capacity of iron (Cp), and the temperature change (ΔT). This substitution will set the stage for the final calculation of the heat required. Plugging in the values, we have:

Q=(55.8g)(0.450J/g⋅°C)(24.0°C) Q = (55.8 g)(0.450 J/g \cdot \degree C)(24.0 \degree C)

Now, we perform the multiplication to obtain the numerical value of Q:

Q=602.64J Q = 602.64 J

This result indicates that 602.64 joules of heat are required to raise the temperature of the iron cube from 25.0°C to 49.0°C. However, we must adhere to the rules of significant figures, as specified in the problem statement.

Step 5: Round to Three Significant Figures

The final step in our solution is to round the calculated value to three significant figures. This ensures that our answer is presented with the appropriate level of precision, reflecting the precision of the given values. The calculated value, 602.64 J, has five significant figures. To round it to three significant figures, we look at the fourth digit (6). Since it is greater than or equal to 5, we round up the third digit.

Therefore, rounding 602.64 J to three significant figures gives us 603 J.

After carefully following our step-by-step solution, we arrive at the final answer. The amount of heat required to raise the temperature of the 55.8 g iron cube from 25.0°C to 49.0°C is:

Q=603J Q = 603 J

This answer is rounded to three significant figures, as requested in the problem statement. It represents the energy input necessary to achieve the desired temperature change in the iron cube.

In this comprehensive article, we have embarked on a journey to calculate the amount of heat required to raise the temperature of an iron cube. We began by establishing a solid foundation of key concepts, including the definition of heat, the significance of specific heat capacity, and the fundamental heat transfer formula. We then systematically worked through the problem, carefully identifying the given values, calculating the temperature change, applying the heat transfer formula, and rounding our final answer to the appropriate number of significant figures.

Our calculation revealed that 603 joules of heat are required to raise the temperature of the 55.8 g iron cube from 25.0°C to 49.0°C. This result underscores the practical application of thermodynamics in everyday scenarios. Understanding heat transfer is crucial in various fields, from engineering to cooking, and mastering these calculations empowers us to make informed decisions and solve real-world problems.

Moreover, this exercise highlights the importance of a systematic approach to problem-solving. By breaking down the problem into manageable steps, we can ensure accuracy and clarity in our solution. This approach is not only valuable in thermodynamics but also applicable to a wide range of scientific and engineering disciplines.

In conclusion, the calculation of heat transfer is a fundamental skill in thermodynamics. By grasping the underlying concepts, applying the appropriate formulas, and adhering to a systematic approach, we can confidently tackle heat transfer problems and gain a deeper appreciation for the role of energy in our world.

Heat Calculation for Iron Cube: Determine the quantity of heat needed to elevate the temperature of a 55.8g iron cube from 25.0°C to 49.0°C.