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A ceramic kiln at 1300 K is made of 12 kg of refractory brick (cbrick=960 J/kg*K)

and is well-insulated (adiabatic) on the outside. A 2 kg clay bowl (cclay=880 J/kg*K) at 300

K is put into the kiln for firing. Inside the kiln there is 0. 7 kg of air initially at 1300 K and 100

kPa. The kiln fire is turned off when the bowl is put into the kiln. Assume that the volume

of the clay bowl and air does not change during firing. Approximate air with constant

properties of Cv= 0. 727 kJ/kgꞏK, CP=1. 014 kJ/kgꞏK, and R=0. 287 kPaꞏm3/kgꞏK.



a. Determine the equilibrium temperature of the system (kiln bricks, clay bowl, and air)

after a long time. Assume the system is isolated and the kiln fire/heating is turned

off when the bowl was added.

b. Find the change in entropy of the system (kiln, bowl, and air) during the process

User SmallB
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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

User Teunbrand
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