An archeologist finds a 1.62 kg goblet that she believes to be made of pure gold. When 1350 cal (5650 J) of heat is added to the goblet, its temperature increases by 7.8 ℃. Calculate the specific heat of the goblet. Is it made of gold? Explain.

Verified step by step guidance

1. Identify the formula for specific heat capacity: \( c = \frac{q}{m \cdot \Delta T} \), where \( q \) is the heat added, \( m \) is the mass, and \( \Delta T \) is the change in temperature.
2. Substitute the given values into the formula: \( q = 5650 \text{ J} \), \( m = 1.62 \text{ kg} \), and \( \Delta T = 7.8 \text{ ℃} \).
3. Calculate the specific heat capacity \( c \) using the substituted values.
4. Compare the calculated specific heat capacity with the known specific heat capacity of gold, which is approximately \( 0.129 \text{ J/g}^\circ\text{C} \) or \( 129 \text{ J/kg}^\circ\text{C} \).
5. Determine if the goblet is made of gold based on whether the calculated specific heat matches the known value for gold.

Key Concepts

Specific Heat Capacity

Specific heat capacity is the amount of heat required to raise the temperature of one gram of a substance by one degree Celsius. It is a material-specific property that helps in understanding how substances respond to heat. The formula to calculate specific heat is given by Q = mcΔT, where Q is the heat added, m is the mass, c is the specific heat capacity, and ΔT is the change in temperature.

Heat Transfer

Heat transfer refers to the movement of thermal energy from one object or substance to another due to a temperature difference. In this context, the heat added to the goblet causes its temperature to rise, which can be quantified using the specific heat capacity. Understanding heat transfer is essential for calculating how much energy is needed to change the temperature of a material.

Comparison with Gold's Specific Heat

To determine if the goblet is made of gold, we need to compare the calculated specific heat of the goblet with the known specific heat of gold, which is approximately 0.129 J/g°C. If the calculated value closely matches this, it supports the hypothesis that the goblet is made of pure gold. This comparison is crucial for validating the archeologist's assumption.