The final equilibrium temperature in the tank.

Question

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Answer 1

Question

Chapter 8, Problem 187RQ

(a)

To determine

The final equilibrium temperature in the tank.

(a)

Expert Solution

Explanation of Solution

Given:

The initial temperature of the water (T1)water is 20°C.

The mass of the ice (mice) is 80 kg.

The initial temperature of the ice (T1)solid is −5°C.

The melting temperature of the water (T1)ice is 0°C.

The heat of fusion of ice (hif) is 333.7 kJ/kg.

Calculation:

Refer Table A-3, “Properties of common liquids, solids, and foods”,

The specific heat at constant pressure at room temperature for water is 4.18 kJ/kg⋅K.

The specific heat at constant pressure at room temperature for ice is 2.11 kJ/kg⋅K.

The melting temperature and the heat of fusion of ice (hif) at 1 atm are 0°C and 333.7 kJ/kg respectively.

Write the expression for the energy balance equation for closed system.

Ein−Eout=ΔEsystem (I)

Here, energy transfer into the control volume is Ein, energy transfer exit from the control volume is Eout and change in internal energy of system is ΔEsystem.

Substitute Ein=0, Eout=0 and ΔEsystem=ΔUice+ΔUwater in Equation (I).

0−0=ΔUice+ΔUwater0={[micecp,ice(0°C−T1)solid+micehif+micecp,ice(T2−0°C)]ice+[mwatercp,water(T2−T1)]water}{(80 kg)[2.11 kJ/kg⋅K(0°C−(−5°C))solid+333.7 kJ/kg+4.18 kJ/kg⋅K(T2−0°C)]ice+[(1000 kg)(4.18 kJ/kg⋅K)(T2−20°C)]water}=0T2=12.42°C

Thus, the final equilibrium temperature in the tank is 12.42°C.

(b)

To determine

The entropy generation during the process.

(b)

Expert Solution

Explanation of Solution

Write the expression for the entropy balance equation of the system.

Sin−Sout+Sgen=ΔSsystem (II)

Here, rate of net entropy in is Sin, rate of net entropy out is Sout, rate of entropy generation is Sgen and change of entropy of the system is ΔSsystem

Substitute Sin=0, Sout=0, and ΔSsystem=ΔSice+ΔSwater in Equation (II).

0−0+Sgen=ΔSice+ΔSwaterSgen=[(micecp,solidln(TmeltingT1)solid+micehifTmelting+micecpln(T2T1)liquid)ice+(mwatercp,waterln(T2T1))water]

Sgen=[mice(cp,solidln(TmeltingT1)solid+hifTmelting+cpln(T2T1)liquid)ice+(mwatercp,waterln(T2T1))water]

Sgen={(80 kg)((2.11 kJ/kg⋅K)ln(0 °C−5 °C)solid+333.7 kJ/kg0 °C+(4.18 kJ/kg⋅K)ln(12.42°C0 °C)liquid)ice+((1000 kg)(4.18 kJ/kg⋅K)ln(12.42°C20 °C))water}

Sgen={(80 kg)((2.11 kJ/kg⋅K)ln((0+273) K(−5+273) K)solid+333.7 kJ/kg0+273 K+(4.18 kJ/kg⋅K)ln((12.42+273) K(0+273) K)liquid)ice+((1000 kg)(4.18 kJ/kg⋅K)ln((12.42+273) K(20+273) K))water}=115.8 kJ/K−109.6 kJ/K=6.2 kJ/K

Thus, the entropy generation during the process is 6.2 kJ/K.

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Answer 2

Question

Chapter 8, Problem 187RQ

(a)

To determine

The final equilibrium temperature in the tank.

(a)

Expert Solution

Explanation of Solution

Given:

The initial temperature of the water (T1)water is 20°C.

The mass of the ice (mice) is 80 kg.

The initial temperature of the ice (T1)solid is −5°C.

The melting temperature of the water (T1)ice is 0°C.

The heat of fusion of ice (hif) is 333.7 kJ/kg.

Calculation:

Refer Table A-3, “Properties of common liquids, solids, and foods”,

The specific heat at constant pressure at room temperature for water is 4.18 kJ/kg⋅K.

The specific heat at constant pressure at room temperature for ice is 2.11 kJ/kg⋅K.

The melting temperature and the heat of fusion of ice (hif) at 1 atm are 0°C and 333.7 kJ/kg respectively.

Write the expression for the energy balance equation for closed system.

Ein−Eout=ΔEsystem (I)

Here, energy transfer into the control volume is Ein, energy transfer exit from the control volume is Eout and change in internal energy of system is ΔEsystem.

Substitute Ein=0, Eout=0 and ΔEsystem=ΔUice+ΔUwater in Equation (I).

0−0=ΔUice+ΔUwater0={[micecp,ice(0°C−T1)solid+micehif+micecp,ice(T2−0°C)]ice+[mwatercp,water(T2−T1)]water}{(80 kg)[2.11 kJ/kg⋅K(0°C−(−5°C))solid+333.7 kJ/kg+4.18 kJ/kg⋅K(T2−0°C)]ice+[(1000 kg)(4.18 kJ/kg⋅K)(T2−20°C)]water}=0T2=12.42°C

Thus, the final equilibrium temperature in the tank is 12.42°C.

(b)

To determine

The entropy generation during the process.

(b)

Expert Solution

Explanation of Solution

Write the expression for the entropy balance equation of the system.

Sin−Sout+Sgen=ΔSsystem (II)

Here, rate of net entropy in is Sin, rate of net entropy out is Sout, rate of entropy generation is Sgen and change of entropy of the system is ΔSsystem

Substitute Sin=0, Sout=0, and ΔSsystem=ΔSice+ΔSwater in Equation (II).

0−0+Sgen=ΔSice+ΔSwaterSgen=[(micecp,solidln(TmeltingT1)solid+micehifTmelting+micecpln(T2T1)liquid)ice+(mwatercp,waterln(T2T1))water]

Sgen=[mice(cp,solidln(TmeltingT1)solid+hifTmelting+cpln(T2T1)liquid)ice+(mwatercp,waterln(T2T1))water]

Sgen={(80 kg)((2.11 kJ/kg⋅K)ln(0 °C−5 °C)solid+333.7 kJ/kg0 °C+(4.18 kJ/kg⋅K)ln(12.42°C0 °C)liquid)ice+((1000 kg)(4.18 kJ/kg⋅K)ln(12.42°C20 °C))water}

Sgen={(80 kg)((2.11 kJ/kg⋅K)ln((0+273) K(−5+273) K)solid+333.7 kJ/kg0+273 K+(4.18 kJ/kg⋅K)ln((12.42+273) K(0+273) K)liquid)ice+((1000 kg)(4.18 kJ/kg⋅K)ln((12.42+273) K(20+273) K))water}=115.8 kJ/K−109.6 kJ/K=6.2 kJ/K

Thus, the entropy generation during the process is 6.2 kJ/K.

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Answer 3

Question

Chapter 8, Problem 187RQ

(a)

To determine

The final equilibrium temperature in the tank.

(a)

Expert Solution

Explanation of Solution

Given:

The initial temperature of the water (T1)water is 20°C.

The mass of the ice (mice) is 80 kg.

The initial temperature of the ice (T1)solid is −5°C.

The melting temperature of the water (T1)ice is 0°C.

The heat of fusion of ice (hif) is 333.7 kJ/kg.

Calculation:

Refer Table A-3, “Properties of common liquids, solids, and foods”,

The specific heat at constant pressure at room temperature for water is 4.18 kJ/kg⋅K.

The specific heat at constant pressure at room temperature for ice is 2.11 kJ/kg⋅K.

The melting temperature and the heat of fusion of ice (hif) at 1 atm are 0°C and 333.7 kJ/kg respectively.

Write the expression for the energy balance equation for closed system.

Ein−Eout=ΔEsystem (I)

Here, energy transfer into the control volume is Ein, energy transfer exit from the control volume is Eout and change in internal energy of system is ΔEsystem.

Substitute Ein=0, Eout=0 and ΔEsystem=ΔUice+ΔUwater in Equation (I).

0−0=ΔUice+ΔUwater0={[micecp,ice(0°C−T1)solid+micehif+micecp,ice(T2−0°C)]ice+[mwatercp,water(T2−T1)]water}{(80 kg)[2.11 kJ/kg⋅K(0°C−(−5°C))solid+333.7 kJ/kg+4.18 kJ/kg⋅K(T2−0°C)]ice+[(1000 kg)(4.18 kJ/kg⋅K)(T2−20°C)]water}=0T2=12.42°C

Thus, the final equilibrium temperature in the tank is 12.42°C.

(b)

To determine

The entropy generation during the process.

(b)

Expert Solution

Explanation of Solution

Write the expression for the entropy balance equation of the system.

Sin−Sout+Sgen=ΔSsystem (II)

Here, rate of net entropy in is Sin, rate of net entropy out is Sout, rate of entropy generation is Sgen and change of entropy of the system is ΔSsystem

Substitute Sin=0, Sout=0, and ΔSsystem=ΔSice+ΔSwater in Equation (II).

0−0+Sgen=ΔSice+ΔSwaterSgen=[(micecp,solidln(TmeltingT1)solid+micehifTmelting+micecpln(T2T1)liquid)ice+(mwatercp,waterln(T2T1))water]

Sgen=[mice(cp,solidln(TmeltingT1)solid+hifTmelting+cpln(T2T1)liquid)ice+(mwatercp,waterln(T2T1))water]

Sgen={(80 kg)((2.11 kJ/kg⋅K)ln(0 °C−5 °C)solid+333.7 kJ/kg0 °C+(4.18 kJ/kg⋅K)ln(12.42°C0 °C)liquid)ice+((1000 kg)(4.18 kJ/kg⋅K)ln(12.42°C20 °C))water}

Sgen={(80 kg)((2.11 kJ/kg⋅K)ln((0+273) K(−5+273) K)solid+333.7 kJ/kg0+273 K+(4.18 kJ/kg⋅K)ln((12.42+273) K(0+273) K)liquid)ice+((1000 kg)(4.18 kJ/kg⋅K)ln((12.42+273) K(20+273) K))water}=115.8 kJ/K−109.6 kJ/K=6.2 kJ/K

Thus, the entropy generation during the process is 6.2 kJ/K.

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Answer 4

Question

Chapter 8, Problem 187RQ

(a)

To determine

The final equilibrium temperature in the tank.

(a)

Expert Solution

Explanation of Solution

Given:

The initial temperature of the water (T1)water is 20°C.

The mass of the ice (mice) is 80 kg.

The initial temperature of the ice (T1)solid is −5°C.

The melting temperature of the water (T1)ice is 0°C.

The heat of fusion of ice (hif) is 333.7 kJ/kg.

Calculation:

Refer Table A-3, “Properties of common liquids, solids, and foods”,

The specific heat at constant pressure at room temperature for water is 4.18 kJ/kg⋅K.

The specific heat at constant pressure at room temperature for ice is 2.11 kJ/kg⋅K.

The melting temperature and the heat of fusion of ice (hif) at 1 atm are 0°C and 333.7 kJ/kg respectively.

Write the expression for the energy balance equation for closed system.

Ein−Eout=ΔEsystem (I)

Here, energy transfer into the control volume is Ein, energy transfer exit from the control volume is Eout and change in internal energy of system is ΔEsystem.

Substitute Ein=0, Eout=0 and ΔEsystem=ΔUice+ΔUwater in Equation (I).

0−0=ΔUice+ΔUwater0={[micecp,ice(0°C−T1)solid+micehif+micecp,ice(T2−0°C)]ice+[mwatercp,water(T2−T1)]water}{(80 kg)[2.11 kJ/kg⋅K(0°C−(−5°C))solid+333.7 kJ/kg+4.18 kJ/kg⋅K(T2−0°C)]ice+[(1000 kg)(4.18 kJ/kg⋅K)(T2−20°C)]water}=0T2=12.42°C

Thus, the final equilibrium temperature in the tank is 12.42°C.

(b)

To determine

The entropy generation during the process.

(b)

Expert Solution

Explanation of Solution

Write the expression for the entropy balance equation of the system.

Sin−Sout+Sgen=ΔSsystem (II)

Here, rate of net entropy in is Sin, rate of net entropy out is Sout, rate of entropy generation is Sgen and change of entropy of the system is ΔSsystem

Substitute Sin=0, Sout=0, and ΔSsystem=ΔSice+ΔSwater in Equation (II).

0−0+Sgen=ΔSice+ΔSwaterSgen=[(micecp,solidln(TmeltingT1)solid+micehifTmelting+micecpln(T2T1)liquid)ice+(mwatercp,waterln(T2T1))water]

Sgen=[mice(cp,solidln(TmeltingT1)solid+hifTmelting+cpln(T2T1)liquid)ice+(mwatercp,waterln(T2T1))water]

Sgen={(80 kg)((2.11 kJ/kg⋅K)ln(0 °C−5 °C)solid+333.7 kJ/kg0 °C+(4.18 kJ/kg⋅K)ln(12.42°C0 °C)liquid)ice+((1000 kg)(4.18 kJ/kg⋅K)ln(12.42°C20 °C))water}

Sgen={(80 kg)((2.11 kJ/kg⋅K)ln((0+273) K(−5+273) K)solid+333.7 kJ/kg0+273 K+(4.18 kJ/kg⋅K)ln((12.42+273) K(0+273) K)liquid)ice+((1000 kg)(4.18 kJ/kg⋅K)ln((12.42+273) K(20+273) K))water}=115.8 kJ/K−109.6 kJ/K=6.2 kJ/K

Thus, the entropy generation during the process is 6.2 kJ/K.

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Answer 5

Chapter 8, Problem 187RQ

(a)

To determine

The final equilibrium temperature in the tank.

(a)

Expert Solution

Explanation of Solution

Given:

The initial temperature of the water (T1)water is 20°C.

The mass of the ice (mice) is 80 kg.

The initial temperature of the ice (T1)solid is −5°C.

The melting temperature of the water (T1)ice is 0°C.

The heat of fusion of ice (hif) is 333.7 kJ/kg.

Calculation:

Refer Table A-3, “Properties of common liquids, solids, and foods”,

The specific heat at constant pressure at room temperature for water is 4.18 kJ/kg⋅K.

The specific heat at constant pressure at room temperature for ice is 2.11 kJ/kg⋅K.

The melting temperature and the heat of fusion of ice (hif) at 1 atm are 0°C and 333.7 kJ/kg respectively.

Write the expression for the energy balance equation for closed system.

Ein−Eout=ΔEsystem (I)

Here, energy transfer into the control volume is Ein, energy transfer exit from the control volume is Eout and change in internal energy of system is ΔEsystem.

Substitute Ein=0, Eout=0 and ΔEsystem=ΔUice+ΔUwater in Equation (I).

0−0=ΔUice+ΔUwater0={[micecp,ice(0°C−T1)solid+micehif+micecp,ice(T2−0°C)]ice+[mwatercp,water(T2−T1)]water}{(80 kg)[2.11 kJ/kg⋅K(0°C−(−5°C))solid+333.7 kJ/kg+4.18 kJ/kg⋅K(T2−0°C)]ice+[(1000 kg)(4.18 kJ/kg⋅K)(T2−20°C)]water}=0T2=12.42°C

Thus, the final equilibrium temperature in the tank is 12.42°C.

(b)

To determine

The entropy generation during the process.

(b)

Expert Solution

Explanation of Solution

Write the expression for the entropy balance equation of the system.

Sin−Sout+Sgen=ΔSsystem (II)

Here, rate of net entropy in is Sin, rate of net entropy out is Sout, rate of entropy generation is Sgen and change of entropy of the system is ΔSsystem

Substitute Sin=0, Sout=0, and ΔSsystem=ΔSice+ΔSwater in Equation (II).

0−0+Sgen=ΔSice+ΔSwaterSgen=[(micecp,solidln(TmeltingT1)solid+micehifTmelting+micecpln(T2T1)liquid)ice+(mwatercp,waterln(T2T1))water]

Sgen=[mice(cp,solidln(TmeltingT1)solid+hifTmelting+cpln(T2T1)liquid)ice+(mwatercp,waterln(T2T1))water]

Sgen={(80 kg)((2.11 kJ/kg⋅K)ln(0 °C−5 °C)solid+333.7 kJ/kg0 °C+(4.18 kJ/kg⋅K)ln(12.42°C0 °C)liquid)ice+((1000 kg)(4.18 kJ/kg⋅K)ln(12.42°C20 °C))water}

Sgen={(80 kg)((2.11 kJ/kg⋅K)ln((0+273) K(−5+273) K)solid+333.7 kJ/kg0+273 K+(4.18 kJ/kg⋅K)ln((12.42+273) K(0+273) K)liquid)ice+((1000 kg)(4.18 kJ/kg⋅K)ln((12.42+273) K(20+273) K))water}=115.8 kJ/K−109.6 kJ/K=6.2 kJ/K

Thus, the entropy generation during the process is 6.2 kJ/K.

Answer 6

Chapter 8, Problem 187RQ

(a)

To determine

The final equilibrium temperature in the tank.

(a)

Expert Solution

Explanation of Solution

Given:

The initial temperature of the water (T1)water is 20°C.

The mass of the ice (mice) is 80 kg.

The initial temperature of the ice (T1)solid is −5°C.

The melting temperature of the water (T1)ice is 0°C.

The heat of fusion of ice (hif) is 333.7 kJ/kg.

Calculation:

Refer Table A-3, “Properties of common liquids, solids, and foods”,

The specific heat at constant pressure at room temperature for water is 4.18 kJ/kg⋅K.

The specific heat at constant pressure at room temperature for ice is 2.11 kJ/kg⋅K.

The melting temperature and the heat of fusion of ice (hif) at 1 atm are 0°C and 333.7 kJ/kg respectively.

Write the expression for the energy balance equation for closed system.

Ein−Eout=ΔEsystem (I)

Here, energy transfer into the control volume is Ein, energy transfer exit from the control volume is Eout and change in internal energy of system is ΔEsystem.

Substitute Ein=0, Eout=0 and ΔEsystem=ΔUice+ΔUwater in Equation (I).

0−0=ΔUice+ΔUwater0={[micecp,ice(0°C−T1)solid+micehif+micecp,ice(T2−0°C)]ice+[mwatercp,water(T2−T1)]water}{(80 kg)[2.11 kJ/kg⋅K(0°C−(−5°C))solid+333.7 kJ/kg+4.18 kJ/kg⋅K(T2−0°C)]ice+[(1000 kg)(4.18 kJ/kg⋅K)(T2−20°C)]water}=0T2=12.42°C

Thus, the final equilibrium temperature in the tank is 12.42°C.

Answer 7

Chapter 8, Problem 187RQ

(a)

To determine

The final equilibrium temperature in the tank.

Answer 8

(a)

Expert Solution

Explanation of Solution

Given:

The initial temperature of the water (T1)water is 20°C.

The mass of the ice (mice) is 80 kg.

The initial temperature of the ice (T1)solid is −5°C.

The melting temperature of the water (T1)ice is 0°C.

The heat of fusion of ice (hif) is 333.7 kJ/kg.

Calculation:

Refer Table A-3, “Properties of common liquids, solids, and foods”,

The specific heat at constant pressure at room temperature for water is 4.18 kJ/kg⋅K.

The specific heat at constant pressure at room temperature for ice is 2.11 kJ/kg⋅K.

The melting temperature and the heat of fusion of ice (hif) at 1 atm are 0°C and 333.7 kJ/kg respectively.

Write the expression for the energy balance equation for closed system.

Ein−Eout=ΔEsystem (I)

Here, energy transfer into the control volume is Ein, energy transfer exit from the control volume is Eout and change in internal energy of system is ΔEsystem.

Substitute Ein=0, Eout=0 and ΔEsystem=ΔUice+ΔUwater in Equation (I).

0−0=ΔUice+ΔUwater0={[micecp,ice(0°C−T1)solid+micehif+micecp,ice(T2−0°C)]ice+[mwatercp,water(T2−T1)]water}{(80 kg)[2.11 kJ/kg⋅K(0°C−(−5°C))solid+333.7 kJ/kg+4.18 kJ/kg⋅K(T2−0°C)]ice+[(1000 kg)(4.18 kJ/kg⋅K)(T2−20°C)]water}=0T2=12.42°C

Thus, the final equilibrium temperature in the tank is 12.42°C.

Answer 9

(a)

Expert Solution

Answer 10

(a)

Expert Solution

Answer 11

Expert Solution

Answer 12

(b)

To determine

The entropy generation during the process.

(b)

Expert Solution

Explanation of Solution

Write the expression for the entropy balance equation of the system.

Sin−Sout+Sgen=ΔSsystem (II)

Here, rate of net entropy in is Sin, rate of net entropy out is Sout, rate of entropy generation is Sgen and change of entropy of the system is ΔSsystem

Substitute Sin=0, Sout=0, and ΔSsystem=ΔSice+ΔSwater in Equation (II).

0−0+Sgen=ΔSice+ΔSwaterSgen=[(micecp,solidln(TmeltingT1)solid+micehifTmelting+micecpln(T2T1)liquid)ice+(mwatercp,waterln(T2T1))water]

Sgen=[mice(cp,solidln(TmeltingT1)solid+hifTmelting+cpln(T2T1)liquid)ice+(mwatercp,waterln(T2T1))water]

Sgen={(80 kg)((2.11 kJ/kg⋅K)ln(0 °C−5 °C)solid+333.7 kJ/kg0 °C+(4.18 kJ/kg⋅K)ln(12.42°C0 °C)liquid)ice+((1000 kg)(4.18 kJ/kg⋅K)ln(12.42°C20 °C))water}

Sgen={(80 kg)((2.11 kJ/kg⋅K)ln((0+273) K(−5+273) K)solid+333.7 kJ/kg0+273 K+(4.18 kJ/kg⋅K)ln((12.42+273) K(0+273) K)liquid)ice+((1000 kg)(4.18 kJ/kg⋅K)ln((12.42+273) K(20+273) K))water}=115.8 kJ/K−109.6 kJ/K=6.2 kJ/K

Thus, the entropy generation during the process is 6.2 kJ/K.

Answer 13

(b)

To determine

The entropy generation during the process.

Answer 14

(b)

Expert Solution

Explanation of Solution

Write the expression for the entropy balance equation of the system.

Sin−Sout+Sgen=ΔSsystem (II)

Here, rate of net entropy in is Sin, rate of net entropy out is Sout, rate of entropy generation is Sgen and change of entropy of the system is ΔSsystem

Substitute Sin=0, Sout=0, and ΔSsystem=ΔSice+ΔSwater in Equation (II).

0−0+Sgen=ΔSice+ΔSwaterSgen=[(micecp,solidln(TmeltingT1)solid+micehifTmelting+micecpln(T2T1)liquid)ice+(mwatercp,waterln(T2T1))water]

Sgen=[mice(cp,solidln(TmeltingT1)solid+hifTmelting+cpln(T2T1)liquid)ice+(mwatercp,waterln(T2T1))water]

Sgen={(80 kg)((2.11 kJ/kg⋅K)ln(0 °C−5 °C)solid+333.7 kJ/kg0 °C+(4.18 kJ/kg⋅K)ln(12.42°C0 °C)liquid)ice+((1000 kg)(4.18 kJ/kg⋅K)ln(12.42°C20 °C))water}

Sgen={(80 kg)((2.11 kJ/kg⋅K)ln((0+273) K(−5+273) K)solid+333.7 kJ/kg0+273 K+(4.18 kJ/kg⋅K)ln((12.42+273) K(0+273) K)liquid)ice+((1000 kg)(4.18 kJ/kg⋅K)ln((12.42+273) K(20+273) K))water}=115.8 kJ/K−109.6 kJ/K=6.2 kJ/K