3 4 1 0 Figure P 3 4 1 0 illustrates a system and fixed control volumic at time t and the system at a short time t later The system temperature is T 3 1 0 9 K at time t and T 3 1 2 6 K at time t t , where t 0 1 s The system mass, m , is 2 9 2 kg , and 1 0 percent of it moves out of the control volume in t 0 1 s The energy per unit mass u is c v T , where c v 1 3 4 1 0 5 J k g K The energy U of the system at any time t is mtilde ( u ) Use the system or Lagrangian approach to evaluate D U D t of the system Compare this result with the D U D t evaluated with that of the material time derivative and flux terms Svstem I has 1 0 of system mass at time t II has 9 0 of system mass at times t and t t III has 1 0 of system mass at time t at time t t 3 4 1 0 Figure P 3 4 1 0 illustrates a system and fixed control volumic at time t and the system at a short time t later The system temperature is T 3 1 0 9 K at time t and T 3 1 2 6 K at time t t , where t 0 1 s The system mass, m , is 2 9 2 kg , and 1 0 percent of it moves out of the control volume in t 0 1 s The energy per unit mass u is c v T , where c v 1 3 4 1 0 5 J k g K The energy U of the system at any time t is mtilde ( u ) Use the system or Lagrangian approach to evaluate D U D t of the system Compare this result with the D U D t evaluated with that of the material time derivative and flux terms Svstem I has 1 0 of system mass at time t II has 9 0 of system mass at times t and t t III has 1 0 of system mass at time t at time t t 3 4 1 0 Figure P 3 4 1 0 illustrates a system and fixed control volumic at time t and the system at a short time t later The system temperature is T 3 1 0 9 K at time t and T 3 1 2 6 K at time t t , where t 0 1 s The system mass, m , is 2 9 2 kg , and 1 0 percent of it moves out of the control volume in t 0 1 s The energy per unit mass u is c v T , where c v 1 3 4 1 0 5 J k g K The energy U of the system at any time t is mtilde ( u ) Use the system or Lagrangian approach to evaluate D U D t of the system Compare this result with the D U D t evaluated with that of the material time derivative and flux terms Svstem I has 1 0 of system mass at time t II has 9 0 of system mass at times t and t t III has 1 0 of system mass at time t at time t t

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Question: 3 . 4 . 1 0 Figure P 3 . 4 . 1 0 illustrates a system and fixed control volumic at time t and

3.4.10

Figure P

3.4.10

illustrates a system and fixed control volumic at time

t

and the system at a short time

t

later. The system temperature is

T = 310.9 K

at time

t

and

T = 312.6 K

at time

t + t,

where

t = 0.1 s .

The system mass,

m,

29.2

,

and

10

percent of it moves out of the control volume in

t = 0.1 s .

The energy per unit mass

u^{}

c_{v} T,

where

c_{v} = 1.34 10^{5} \frac{J}{k} g * K .

The energy

U

of the system at any time

t

is mtilde

(u) .

Use the system or Lagrangian approach to evaluate

D \frac{U}{D} t

of the system. Compare this result with the

D \frac{U}{D} t

evaluated with that of the material time derivative and flux terms.

Svstem

I has

10 %

of system mass at time

t .

II has

90 %

of system mass at times

t

and

t + t .

III has

10 %

of system mass at time

t + .

at time

t + t

3.4.10

Figure P

3.4.10

illustrates a system and fixed control volumic at time

t

and the system at a short time

t

later. The system temperature is

T = 310.9 K

at time

t

and

T = 312.6 K

at time

t + t,

where

t = 0.1 s .

The system mass,

m,

29.2

,

and

10

percent of it moves out of the control volume in

t = 0.1 s .

The energy per unit mass

u^{}

c_{v} T,

where

c_{v} = 1.34 10^{5} \frac{J}{k} g * K .

The energy

U

of the system at any time

t

is mtilde

(u) .

Use the system or Lagrangian approach to evaluate

D \frac{U}{D} t

of the system. Compare this result with the

D \frac{U}{D} t

evaluated with that of the material time derivative and flux terms.

Svstem

I has

10 %

of system mass at time

t .

II has

90 %

of system mass at times

t

and

t + t .

III has

10 %

of system mass at time

t + .

at time

t + t

3.4.10

Figure P

3.4.10

illustrates a system and fixed control volumic at time

t

and the system at a short time

t

later. The system temperature is

T = 310.9 K

at time

t

and

T = 312.6 K

at time

t + t,

where

t = 0.1 s .

The system mass,

m,

29.2

,

and

10

percent of it moves out of the control volume in

t = 0.1 s .

The energy per unit mass

u^{}

c_{v} T,

where

c_{v} = 1.34 10^{5} \frac{J}{k} g * K .

The energy

U

of the system at any time

t

is mtilde

(u) .

Use the system or Lagrangian approach to evaluate

D \frac{U}{D} t

of the system. Compare this result with the

D \frac{U}{D} t

evaluated with that of the material time derivative and flux terms.

Svstem

I has

10 %

of system mass at time

t .

II has

90 %

of system mass at times

t

and

t + t .

III has

10 %

of system mass at time

t + .

at time

t + t

3 . 4 . 1 0 Figure P 3 . 4 . 1 0 illustrates a

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