Answer :
Final answer:
The specific heat capacity of quartz can be calculated using the principle of conservation of energy and the definitions of heat capacity and specific heat. In this experiment, both water and quartz are exchanging heat until they reach a steady temperature. This results in equations for heat loss and gain which can be used to solve for the specific heat capacity of quartz.
Explanation:
In this experiment, we use the principle of conservation of energy and the definitions of heat capacity and specific heat to calculate the specific heat capacity of quartz. Since the quartz and the water are both exchanging heat until they reach a steady temperature, we can utilize the equation Q = mcΔT (where Q is heat energy, m is mass, c is the specific heat capacity and ΔT is the change in temperature).
For the water (remember the specific heat of water is 4.184 J/g °C), we have: Q = mwatercwaterΔTwater = 300.0g * 4.184 J/g °C * (19.3 °C - 17.0 °C)
For the quartz, given it is cooling down, we have an equivalent heat loss: Q = mquartzcquartzΔTquartz. Because the total heat gained by the water is equal to the total heat lost by the quartz (assuming no heat loss to the surrounding), we can solve for cquartz.
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To find the specific heat capacity of quartz, we calculate the heat gained by the water and use the conservation of energy to determine the heat lost by the quartz. The specific heat capacity of quartz is approximately 0.71 J/g°C.
Calculating the Specific Heat Capacity of Quartz
To determine the specific heat capacity of quartz, we will use the principle of conservation of energy, where the heat lost by the quartz will equal the heat gained by the water.
Calculate the heat gained by the water:
- The formula to calculate heat is q = m × c × ΔT, where q is heat, m is mass, c is specific heat capacity, and ΔT is the change in temperature.
For the water:
- (m)water = 300.0 g
- (c)water = 4.184 J/g°C (specific heat capacity of water)
- ΔTwater = 19.3°C - 17.0°C = 2.3°C
- Thus, (q)water = 300.0 g * 4.184 J/g°C × 2.3°C = 2889.6 J
The heat lost by the quartz: According to the law of conservation of energy, the heat lost by the quartz will equal the heat gained by the water. Therefore, (q)quartz = -2890 J (approximated to 2 significant digits).
Determine the specific heat capacity of quartz:
- Rearrange the specific heat formula q = m × c × ΔT to solve for c.
For the quartz:
- (m)quartz = 51.9 g
- ΔTquartz = 97.8°C - 19.3°C = 78.5°C
Thus,
- (c)quartz = (q)quartz / (m × ΔT) = -2890 J / (51.9 g × 78.5°C) ≈ 0.71 J/g°C
Therefore, the specific heat capacity of quartz is 0.71 J/g°C when rounded to 2 significant digits.