Question

The specific heat capacity of gold is \(0.13 \mathrm{J} / \mathrm{g}^{\circ} \mathrm{C} .\) Calculate the specific heat capacity of gold in \(\mathrm{cal} / \mathrm{g}^{\circ} \mathrm{C}\).

Short answer

The specific heat capacity of gold in cal/g°C is approximately \(0.0311\) cal/g°C.

Step-by-step solution

Understand the units and conversion factors

We are asked to convert the specific heat capacity of gold from J/g°C to cal/g°C. To do this, we need to know the conversion factor between Joules and calories. 1 calorie (cal) is defined as the amount of energy required to raise the temperature of 1 gram of water by 1 degree Celsius. It is equivalent to 4.184 Joules (J). The conversion factor from Joules to calories is: 1 cal = 4.184 J.

Convert the given specific heat capacity in J/g°C to cal/g°C

We have the specific heat capacity of gold in J/g°C, which is 0.13 J/g°C. To convert it to cal/g°C, we need to divide it by the conversion factor from the previous step: Specific Heat Capacity (cal/g°C) = Specific Heat Capacity (J/g°C) / Conversion factor from J to cal In our case: Specific Heat Capacity (cal/g°C) = \( \frac{0.13\,\text{J/g}^\circ \text{C}}{4.184\,\text{J/cal}} \)

Calculate the specific heat capacity of gold in cal/g°C

Now, we simply perform the calculation to get the desired specific heat capacity of gold in cal/g°C: Specific Heat Capacity (cal/g°C) = \( \frac{0.13}{4.184} \) cal/g°C ≈ 0.0311 cal/g°C So, the specific heat capacity of gold in cal/g°C is approximately 0.0311 cal/g°C.

Key concepts

Unit Conversion

Unit conversion is a process of changing a measure expressed in one unit to an equivalent measure in another unit. This is crucial in scientific calculations where different systems of measurement might be used. Understanding this process allows you to accurately communicate and work with data such as energy, temperature, and mass regardless of the units used.

For instance, when working with the specific heat capacity of gold, it might be given in joules per gram per degree Celsius (\(\text{J/g}^\circ \text{C}\)). If your experiment or comparison requires the value in calories per gram per degree Celsius (\(\text{cal/g}^\circ \text{C}\)), you must convert from joules to calories, as demonstrated in the exercise solver.

Successfully converting units means recognizing the conversion factor between the initial and desired units. In thermal physics, particularly involving specific heat capacities, these conversions are key to making sense of your calculations and ensuring their accuracy.

Calorie to Joule Conversion

Converting calorie to joule and vice versa is a common practice in thermal physics because both are units of energy. A calorie is a unit that describes the amount of energy necessary to raise the temperature of 1 gram of water by 1 degree Celsius. One calorie is exactly 4.184 joules.

This conversion factor is vital for calculations involving energy changes, especially when comparing results across different scientific fields or contexts. In our example, to convert the specific heat capacity of gold from joules (\(0.13\text{ J/g}^\circ \text{C}\)) to calories, you would divide by 4.184. This effectively changes the energy unit, retaining the physical meaning of the value but in the specified measurement system.

• 1 calorie (cal) = 4.184 joules (J)
• To convert J to cal: Divide by 4.184
• To convert cal to J: Multiply by 4.184

Remembering these conversions enables efficient communication and comprehension in scientific analyses.

Thermal Properties of Gold

The thermal properties of gold, like specific heat capacity, describe how the material absorbs and retains heat. Specific heat capacity is defined as the amount of heat energy required to raise the temperature of one gram of a substance by one degree Celsius.

Gold has a specific heat capacity of \(0.13 \text{ J/g}^\circ \text{C}\), which is equivalent to approximately \(0.0311 \text{ cal/g}^\circ \text{C}\). This means that gold heats up relatively quickly compared to substances with higher specific heat capacities because it requires less energy to increase its temperature.

• Specific Heat Capacity: Amount of heat per unit mass to increase the temperature by 1 °C.
• Low values mean quicker temperature change with same energy input.
• Gold is efficient at conducting heat.

Understanding these properties helps in applications where thermal management is critical, such as using gold in electronics or temperature sensors.