Answer:
To solve this problem, we can apply the principle of energy conservation and the first law of thermodynamics.
a. To determine the equilibrium temperature of the system, we need to consider the heat transfer between the kiln brick, clay bowl, and air. Since the kiln is well-insulated, there is no heat transfer between the kiln and the surroundings, so we can assume the temperature of the kiln brick remains constant at 1300 K.
We can calculate the initial energy of the clay bowl and air as well as the final energy after reaching equilibrium. The energy equation is given by:
Initial energy + Heat transferred = Final energy
The initial energy is the sum of the energy of the clay bowl and the energy of the air:
Initial energy = energy of clay bowl + energy of air
energy of clay bowl = m_clay * c_clay * T_clay
= 2 kg * 880 J/kg*K * 300 K
= 1,320,000 J
energy of air = m_air * Cv * T_air
= 0.7 kg * 0.727 kJ/kg*K * 1300 K
= 828.41 kJ
Initial energy = 1,320,000 J + 828,410 J
= 2,148,410 J
The heat transferred can be calculated as the heat absorbed by the clay bowl and air, and it can be expressed as:
Heat transferred = heat absorbed by clay bowl + heat absorbed by air
The heat absorbed by the clay bowl can be calculated using the specific heat capacity (c_clay) and the change in temperature (T_change):
heat absorbed by clay bowl = m_clay * c_clay * T_change
= 2 kg * 880 J/kg*K * (1300 K - 300 K)
= 2,156,000 J
The heat absorbed by the air can be calculated using the specific heat capacity at constant volume (Cv) and the change in temperature (T_change):
heat absorbed by air = m_air * Cv * T_change
= 0.7 kg * 0.727 kJ/kg*K * (1300 K - 300 K)
= 89.19 kJ
Heat transferred = 2,156,000 J + 89,190 J
= 2,245,190 J
Now, we can calculate the final energy after reaching equilibrium:
Final energy = Initial energy + Heat transferred
= 2,148,410 J + 2,245,190 J
= 4,393,600 J
Since energy is conserved, the final energy is equal to the initial energy at equilibrium, so
Final energy = energy of kiln brick + energy of clay bowl + energy of air
energy of kiln brick = m_brick * c_brick * T_brick
= 12 kg * 960 J/kg*K * 1300 K
= 15,552,000 J
Total energy of the system = energy of kiln brick + energy of clay bowl + energy of air
= 15,552,000 J + 1,320,000 J + 828,410 J
= 17,700,410 J
Now we can set the final energy equal to the total energy:
Total energy = Final energy
17,700,410 J = 4,393,600 J + energy of kiln brick
energy of kiln brick = 13,306,810 J
Since the kiln is well-insulated, there is no heat transfer between the kiln brick and the surroundings. Therefore, the temperature of the kiln brick remains constant at 1300 K.
b. To find the change in entropy of the system during the process, we can use the equation:
Change in entropy = Heat transferred / Temperature
The heat transferred is known to be 2,245,190 J. To calculate the temperature, we can use the ideal gas equation:
PV = mRT
Rearranging the equation to solve for temperature (T):
T = PV / (mR)
= (100 kPa * 0.7 kg) / (0.7 kg * 0.287 kPa*m^3/kg*K)
= 244.36 K
Therefore, the change in entropy is:
Change in entropy = 2,245,190 J / 244.36 K
= 9,195.62 J/K