100 g piece of granite and a 100 g piece of lead are placed in an oven that is at 100°C. The initial temperature of the pieces are 25°C. After a couple of minutes, neither one is at 100°C, but which one is warmer? Which one will reach 100°C first? How much energy will it take for both of the objects to reach 100°C?
To determine which object is warmer and which one will reach 100°C first, we need to understand how heat transfer works. The equation that governs heat transfer is known as the heat equation:
Q = mcΔT
Q represents the amount of heat transferred, m represents the mass of the object, c represents the specific heat capacity of the material, and ΔT represents the change in temperature.
In this case, we have a 100 g piece of granite and a 100 g piece of lead, both starting at 25°C and placed in an oven that is at 100°C. Let's evaluate the heat equation for each object:
For the granite:
Q_granite = m_granite * c_granite * ΔT_granite.
For the lead:
Q_lead = m_lead * c_lead * ΔT_lead.
To determine which object is warmer, we need to compare the final temperatures of the two objects.
Since the initial temperature is 25°C and the oven temperature is 100°C, we can calculate the ΔT for each object as follows:
ΔT_granite = 100°C - 25°C = 75°C.
ΔT_lead = 100°C - 25°C = 75°C.
Now, we need to consider the specific heat capacity of each material. Granite has a specific heat capacity of approximately 0.79 J/g°C, while lead has a specific heat capacity of about 0.13 J/g°C.
Calculating the heat transfer for each object:
Q_granite = m_granite * c_granite * ΔT_granite
= 100 g * 0.79 J/g°C * 75°C
= 5925 J.
Q_lead = m_lead * c_lead * ΔT_lead
= 100 g * 0.13 J/g°C * 75°C
= 975 J.
From these calculations, we can determine that the granite will be warmer since it requires more energy to heat up (Q_granite = 5925 J), compared to the lead (Q_lead = 975 J).
As for which object will reach 100°C first, both objects will reach the same temperature eventually since they are in the same oven at the same temperature. However, granite will take longer to reach 100°C than lead due to its higher heat capacity. The time it takes for both objects to reach 100°C will depend on various factors such as their surface area and the efficiency of heat transfer in the oven.
In summary:
- The granite piece is warmer because it requires more energy to heat up.
- The lead piece will reach 100°C first since it has a lower specific heat capacity and requires less energy to heat up.
- It would require 5925 J of energy for the granite and 975 J for the lead to reach 100°C.