To determine the heat capacity of the system S, we can use the information provided about the heating and cooling processes. The heat capacity is a measure of how much heat energy is required to change the temperature of a substance by a certain amount. In this case, we can analyze the cooling phase to find the heat capacity.
Understanding the Cooling Process
When the heater is switched off, the system S cools from 35.1 °C to 34.9 °C in one minute. This temperature change is crucial for calculating the heat capacity. The formula we will use is:
Where:
- Q is the heat lost by the system.
- C is the heat capacity of the system.
- ΔT is the change in temperature.
Calculating the Heat Lost
First, we need to find the heat lost (Q) during the cooling process. The temperature change (ΔT) is:
- ΔT = T_initial - T_final = 35.1 °C - 34.9 °C = 0.2 °C
Next, we need to convert this temperature change into Kelvin, but since the size of the degree is the same, we can use the Celsius change directly. Now, we need to find the heat lost in joules. Since the cooling happens over one minute, we can relate this to the power of the heater:
- The heater has a power of 10 W, which means it provides 10 joules of energy per second.
- In one minute (60 seconds), the total energy provided by the heater is: Q = Power × Time = 10 W × 60 s = 600 J.
Relating Heat Lost to Temperature Change
Now we can substitute the values into the heat loss equation. The heat lost (Q) during the cooling process is equal to the energy that the system would have lost to cool down by 0.2 °C:
- Q = C × ΔT
- 600 J = C × 0.2 °C
Solving for Heat Capacity
Now, we can solve for C:
- C = Q / ΔT = 600 J / 0.2 °C = 3000 J/°C.
This means the heat capacity of the system S is 3000 J/°C. This value indicates how much energy is required to raise the temperature of the system by one degree Celsius.
Final Thoughts
In summary, by analyzing the cooling process and applying the relationship between heat, heat capacity, and temperature change, we determined that the heat capacity of system S is 3000 J/°C. This calculation illustrates the principles of thermodynamics and energy transfer in a practical scenario.
