Answer:
See explanation
Explanation:
Notice that the condenser section includes both the hot water and space heater and station (3) is specified as being in the Quality region. Assume that 50°C is a reasonable maximum hot water temperature for home usage, thus at a high pressure of 1.6 MPa, the maximum power available for hot water heating will occur when the refrigerant at station (3) reaches the saturated liquid state. (Quick Quiz: justify this statement). Assume also that the refrigerant at station (4) reaches a subcooled liquid temperature of 20°C while heating the air.
Using the conditions shown on the diagram and assuming that station (3) is at the saturated liquid state
a) On the P-h diagram provided below carefully plot the five processes of the heat pump together with the following constant temperature lines: 50°C (hot water), 13°C (ground loop), and -10°C (outside air temperature)
b) Using the R134a property tables determine the enthalpies at all five stations and verify and indicate their values on the P-h diagram.
c) Determine the mass flow rate of the refrigerant R134a. [0.0127 kg/s]
d) Determine the power absorbed by the hot water heater [2.0 kW] and that absorbed by the space heater [0.72 kW].
e) Determine the time taken for 100 liters of water at an initial temperature of 20°C to reach the required hot water temperature of 50°C [105 minutes].
f) Determine the Coefficient of Performance of the hot water heater [COPHW = 4.0] (defined as the heat absorbed by the hot water divided by the work done on the compressor)
g) Determine the Coefficient of Performance of the heat pump [COPHP = 5.4] (defined as the total heat rejected by the refrigerant in the hot water and space heaters divided by the work done on the compressor)
h) What changes would be required of the system parameters if no geothermal water loop was used, and the evaporator was required to absorb its heat from the outside air at -10°C. Discuss the advantages of the geothermal heat pump system over other means of space and water heating
Answers:
a) 
b) 
c) 
Explanation:
<h3>a) Mass of the continent</h3>
Density
is defined as a relation between mass
and volume
:
(1)
Where:
is the average density of the continent
is the mass of the continent
is the volume of the continent, which can be estimated is we assume it as a a slab of rock 5300 km on a side and 37 km deep:

Finding the mass:
(2)
(3)
(4) This is the mass of the continent
<h3>b) Kinetic energy of the continent</h3>
Kinetic energy
is given by the following equation:
(5)
Where:
is the mass of the continent
is the velocity of the continent
(6)
(7) This is the kinetic energy of the continent
<h3>c) Speed of the jogger</h3>
If we have a jogger with mass
and the same kinetic energy as that of the continent
, we can find its velocity by isolating
from (5):
(6)
Finally:
This is the speed of the jogger
Answer:
Part a)

Part b)

Part c)
distance L is independent of the mass of the sphere
Explanation:
Part a)
As we know that rotational kinetic energy of the sphere is given as

so we will have

so we will have




Part b)
By mechanical energy conservation law we know that
Work done against gravity = initial kinetic energy of the sphere
So we will have



Part c)
by equation of energy conservation we know that

so here we can see that distance L is independent of the mass of the sphere