Thermal Energy Transfer and Specific Heat: Calculating the Specific Heat of Iron
The concept of thermal energy transfer involves the movement of heat energy from a hotter object to a cooler one until thermal equilibrium is reached. This principle is fundamental in understanding the behavior of materials under different temperatures. This article will demonstrate how to calculate the specific heat of iron using a principle of conservation of energy, and it will also provide a step-by-step mathematical explanation with real-world data.
Experiment Overview
An experiment involves a 1.22-kg (1220 g) piece of iron at an initial temperature of 126.5 °C being dropped into 981 g of water at an initial temperature of 22.1 °C. After heat exchange, the final temperature is measured to be 34.4 °C. From this data, we can deduce the specific heat of iron using the principle of conservation of energy.
Key Data and Formulas
Mass of iron (mFe): 1.22 kg (1220 g) Initial temperature of iron (TiFe): 126.5 °C Final temperature (Tf): 34.4 °C Mass of water (mwater): 981 g Initial temperature of water (Tiwater): 22.1 °C Specific heat of water (cwater): 4.18 J g-1°C-1 Heat lost by iron (qFe): mFe × cFe × (TiFe - Tf) Heat gained by water (qwater): mwater × cwater × (Tf - Tiwater)Mathematical Calculation
The heat gained by the water can be calculated using the formula:
[ q_{water} m_{water} cdot c_{water} cdot (T_f - T_{iwater}) ]
Substituting the values given:
[ q_{water} 981 text{g} cdot 4.18 text{J g}^{-1} text{°C}^{-1} cdot (34.4 text{°C} - 22.1 text{°C}) ]
Calculating the change in temperature for the water:
[ T_f - T_{iwater} 12.3 text{°C} ]
Substitute this back into the equation for qwater:
[ q_{water} 981 text{g} cdot 4.18 text{J g}^{-1} text{°C}^{-1} cdot 12.3 text{°C} ]
Calculating this:
[ q_{water} approx 49174.47 text{J} ]
The heat lost by the iron can be expressed as:
[ q_{Fe} m_{Fe} cdot c_{Fe} cdot (T_{iFe} - T_f) ]
Where cFe is the specific heat of iron. The change in temperature for the iron is:
[ T_{iFe} - T_f -92.1 text{°C} ]
Setting the heat gained by the water equal to the heat lost by the iron:
[ q_{water} -q_{Fe} ]
Substituting the equations:
[ 49174.47 text{J} 1220 text{g} cdot c_{Fe} cdot -92.1 text{°C} ]
Solving for cFe and rearranging the equation:
[ c_{Fe} frac{49174.47 text{J}}{1220 text{g} cdot -92.1 text{°C}} ]
Calculating this:
[ c_{Fe} approx -0.436 text{J g}^{-1} text{°C}^{-1} ]
Since specific heat cannot be negative, we take the absolute value:
[ c_{Fe} approx 0.436 text{J g}^{-1} text{°C}^{-1} ]
Conclusion
Through the application of the principle of conservation of energy, it is determined that the specific heat of iron is approximately 0.436 J g-1°C-1. This result can be useful in various applications, such as in engineering, material science, and practical thermodynamics problems.
Note: This calculation assumes ideal conditions and neglects any losses due to the environment. For precise measurements in real-world scenarios, additional factors may need to be considered.
Understanding the specific heat of materials is crucial in a wide range of practical applications. By applying the principle of conservation of energy, we can derive the specific heat of iron, an essential property in numerous fields.