Textbook Question
On a hot day, the beach sand gets hot but the water stays cool. Would you predict that the specific heat of sand is higher or lower than that of water? Explain. (3.6)
1896
views
3. Matter and Energy
Heat Capacity
1:37 minutesProblem 109
Textbook Question
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 guidance1
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.
Substitute the given values into the formula: \( q = 5650 \text{ J} \), \( m = 1.62 \text{ kg} \), and \( \Delta T = 7.8 \text{ ℃} \).
Calculate the specific heat capacity \( c \) using the substituted values.
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 \( 129 \text{ J/kg}^\circ\text{C} \).
Determine if the goblet is made of gold based on whether the calculated specific heat matches the known value for gold.
Verified video answer for a similar problem:This video solution was recommended by our tutors as helpful for the problem above
Video duration:
1mKey Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
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.
Recommended video:
Guided course
02:19
Heat Capacity
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.
Recommended video:
Guided course
02:19Heat Capacity
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.
Recommended video:
Guided course
02:19Heat Capacity
Related Videos
Related Practice