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luda_lava [24]
3 years ago
12

Water, initially saturated vapor at 4 bar, fills a closed, rigid container. The water is heated until its temperature is 360°C.

For the water, determine the heat transfer, in kJ per kg of water. Kinetic and potential energy effects can be ignored.
Physics
1 answer:
salantis [7]3 years ago
4 0

Explanation:

Using table A-3, we will obtain the properties of saturated water as follows.

Hence, pressure is given as p = 4 bar.

u_{1} = u_{g} = 2553.6 kJ/kg

v_{1} = v_{g} = 0.4625 m^{3}/kg

At state 2, we will obtain the properties. In a closed rigid container, the specific volume will remain constant.

Also, the specific volume saturated vapor at state 1 and 2 becomes equal. So, v_{2} = v_{g} = 0.4625 m^{3}/kg

According to the table A-4, properties of superheated water vapor will obtain the internal energy for state 2 at v_{2} = v_{g} = 0.4625 m^{3}/kg and temperature T_{2} = 360^{o}C so that it will fall in between range of pressure p = 5.0 bar and p = 7.0 bar.

Now, using interpolation we will find the internal energy as follows.

 u_{2} = u_{\text{at 5 bar, 400^{o}C}} + (\frac{v_{2} - v_{\text{at 5 bar, 400^{o}C}}}{v_{\text{at 7 bar, 400^{o}C - v_{at 5 bar, 400^{o}C}}}})(u_{at 7 bar, 400^{o}C - u_{at 5 bar, 400^{o}C}})

     u_{2} = 2963.2 + (\frac{0.4625 - 0.6173}{0.4397 - 0.6173})(2960.9 - 2963.2)

                   = 2963.2 - 2.005

                   = 2961.195 kJ/kg

Now, we will calculate the heat transfer in the system by applying the equation of energy balance as follows.

      Q - W = \Delta U + \Delta K.E + \Delta P.E ......... (1)

Since, the container is rigid so work will be equal to zero and the effects of both kinetic energy and potential energy can be ignored.

            \Delta K.E = \Delta P.E = 0

Now, equation will be as follows.

           Q - W = \Delta U + \Delta K.E + \Delta P.E

           Q - 0 = \Delta U + 0 + 0

           Q = \Delta U

Now, we will obtain the heat transfer per unit mass as follows.

          \frac{Q}{m} = \Delta u

         \frac{Q}{m} = u_{2} - u_{1}

                      = (2961.195 - 2553.6)

                      = 407.595 kJ/kg

Thus, we can conclude that the heat transfer is 407.595 kJ/kg.

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1) At the top, the ball has more potential energy

2) Halfway through the fall, potential energy and kinetic energy are equal

3) Before hitting the ground, the ball has more kinetic energy

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5) Potential energy halfway through the fall: 392 J

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Explanation:

1)

The potential energy of an object is the energy possessed by the object due to its position in a gravitational field. It is given by

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The kinetic energy of an object is the energy possessed by the object due to its motion, and it is given by

KE=\frac{1}{2}mv^2

where v is the speed of the object

For the bowling ball in the problem, when it sits on top of the building it has no kinetic energy (because its speed is zero, v = 0), therefore it has more potential energy than kinetic energy.

2)

The total mechanical energy of the ball, which is the sum of the potential and the kinetic energy, is constant during the fall:

E=PE+KE=const.

When the ball is at the top, all its energy is potential energy, since the kinetic energy is zero:

E=PE=mgH

where H is the initial height.

When the ball is halfway through the fall, the height is H/2, so:

PE=mg\frac{H}{2}

which means that the potential energy is now half of the total mechanical energy: but since the total energy must be constant, this means that the kinetic energy is now also half of the total energy. Therefore, potential energy and kinetic energy are equal.

3)

When the ball is just before hitting the ground, the height of the ball is now zero

h = 0

This also means that the potential energy is zero

PE = 0

Therefore, all the energy of the ball is now kinetic energy:

KE=E

which means that the kinetic energy is maximum, and therefore it is larger than the potential energy: this is because the ball accelerates during the fall, and therefore its speed is maximum just before hitting the ground.

4)

The potential energy of the ball is given by

PE=mgh

where

m is the mass of the object

g is the acceleration of gravity

h is the height of the object above the ground

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Learn more about kinetic and potential energy:

brainly.com/question/6536722

brainly.com/question/1198647

brainly.com/question/10770261

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