Answer:
a. 12.12°
b. 412.04 N
Explanation:
Along vertical axis, the equation can be written as
T_1 sin14 + T_2sinA = mg
T_2sinA = mg - T_1sin12.5 ....................... (a)
Along horizontal axis, the equation can be written as
T_2×cosA = T_1×cos12.5 ......................... (b)
(a)/(b) given us
Tan A = (mg - T_1sin12.5) / T_1 cos12.5
= (176 - 413sin12.5) / 413×cos12.5
A = 12.12 °
(b) T2 cosA = T1 cos12.5
T2 = 413cos12.5/cos12.12
= 412.04 N
Answer:
There is a loss of fluid in the container of 0.475L
Explanation:
To solve the problem it is necessary to take into account the concepts related to the change of voumen in a substance depending on the temperature.
The formula that describes this thermal expansion process is given by:

Where,
Change in volume
Initial Volume
Change in temperature
coefficient of volume expansion (Coefficient of copper and of the liquid for this case)
There are two types of materials in the container, liquid and copper, so we have to change the amount of Total Volume that would be subject to,

Where,
= Change in the volume of liquid
= Change in the volume of copper
Then replacing with the previous equation we have:


Our values are given as,
Thermal expansion coefficient for copper and the liquid to 20°C is




Replacing we have that,



Therefore there is a loss of fluid in the container of 0.475L
Boyle's law says that the volume of a gas varies inversely with the pressure. When the volume of a certain gas is 4l , the pressure is 720 kpa (kilopascals). What is the pressure when the volume is 10l ?
Answer:
a) the magnitude of r is 184.62
b) the direction is 37.74° south of the negative x-axis
Explanation:
Given the data in the question;
as illustrated in the image blow;
To find the the magnitude of r, we will use the Pythagoras theorem
r² = y² + x²
r = √( y² + x²)
we substitute
r = √((-113)² + (-146)²)
r = √(12769 + 21316 )
r = √(34085 )
r = 184.62
Therefore, the magnitude of r is 184.62
To find its direction, we need to find ∅
from SOH CAH TOA
tan = opposite / adjacent
tan∅ = -113 / -146
tan∅ = 0.77397
∅ = tan⁻¹( 0.77397 )
∅ = 37.74°
Therefore, the direction is 37.74° south of the negative x-axis
Complete Question
A certain refrigerator, operating between temperatures of -8.00°C and +23.2°C, can be approximated as a Carnot refrigerator.
What is the refrigerator's coefficient of performance? COP
(b) What If? What would be the coefficient of performance if the refrigerator (operating between the same temperatures) was instead used as a heat pump? COP
Answer:
a

b
Explanation:
From the question we are told that
The lower operation temperature of refrigerator is
The upper operation temperature of the refrigerator is 
Generally the refrigerators coefficient of performance is mathematically represented as

=> 
=> 
Generally if a refrigerator (operating between the same temperatures) was instead used as a heat pump , the coefficient of performance is mathematically represented as
=>
=>