Calculate 8:51 AM.ension in the string (a) before and (b) after the metal 3G
K/S
10. Water flows through a fire hose of diameter 6.35cm at a rate of 0.0120m3/s. The fire hose ends in a nozzle of inner diameter 2.20cm. What is the speed with which the water exits the nozzle?
11. Through a pipe 15.0cm in diameter, water is pumped from the Gefersa River up to Burayu town, located on the west side of Addis Ababa. Suppose, the river is at an elevation of 564m, and the village is at an elevation of 2096m. (a) What is the minimum pressure at which the water must be pumped if it is to arrive at the town? (b) If 4500m³ are pumped per day, what is the speed of the water in the pipe?
12. On an unknown temperature scale, the freezing point of water is -15.0°U and the boiling point is +60.0°U. Develop a linear conversion equation between this temperature scale and the Fahrenheit scale.
13. A copper telephone wire has essentially no sag between poles 35.0 m apart on a winter day when the temperature is -20.0°C. How much longer is the wire on a summer day when T-35.0°C?
14. Calculate the quantity of heat required to raise the temperature of 10g of ice from-10°C to steam 110°C and draw the graph of Temperature (°c) versus Heat (Joule or Cal.)
15. A 1.00-kg block of copper at 20.0°C is dropped into a large vessel of liquid nitrogen at 77.3 K. How many kilograms of nitrogen boil away by the time the copper reaches 77.3K? (The specific heat of copper is 0.0920cal/g°C. The latent heat of vaporization of nitrogen is 48.0cal/g.)
10. The speed with which the water exits the nozzle can be calculated using the equation of continuity:
A1V1 = A2V2
Where A1 and A2 are the cross-sectional areas of the fire hose and the nozzle respectively, and V1 and V2 are the velocities of the water in the hose and the nozzle.
Given:
- Diameter of fire hose = 6.35 cm
- Diameter of nozzle = 2.20 cm
- Flow rate of water = 0.0120 m³/s
Calculating the cross-sectional areas:
A1 = π(6.35/2)² = 31.65 cm² = 0.003165 m²
A2 = π(2.20/2)² = 3.80 cm² = 0.00038 m²
Substitute the values into the equation of continuity:
0.003165 m² * V1 = 0.00038 m² * V2
V2 = (0.003165/0.00038) * V1
V2 = 8.34 * V1
Therefore, the speed with which the water exits the nozzle is 8.34 times the speed at which it flows through the fire hose.
11.
(a) To calculate the minimum pressure at which the water must be pumped if it is to arrive at the town, we can use the Bernoulli's equation:
P + 1/2ρv² + ρgh = constant
Where:
P = pressure
ρ = density of water
v = speed of the water in the pipe
g = acceleration due to gravity
h = height difference
Given:
- Diameter of the pipe = 15.0 cm
- Density of water = 1000 kg/m³
- Acceleration due to gravity = 9.81 m/s²
- Elevation difference = 2096 m - 564 m = 1532 m
Calculate the speed of the water in the pipe (v):
Q = A * v
0.4500 m³/day = (π/4)(0.15 m)² * v
v = 1.039 m/s
Substitute the known values into the Bernoulli's equation to solve for the minimum pressure (P) at which the water must be pumped.
(b) To find the speed of the water in the pipe if 4500m³ are pumped per day, we have already calculated it in part (a) as 1.039 m/s.
12. To develop a linear conversion equation between the unknown temperature scale (U) and the Fahrenheit scale (F), we can use the given freezing and boiling points:
-15°C = - 5°F
60°C = 140°F
We can calculate the slope (m) and y-intercept (b) of the linear equation using two-point form:
m = (140 - (-5)) / (60 - (-15)) = 145 / 75
b = -5 - (m * (-15))
Therefore, the linear conversion equation is:
F = (145/75)*U + [b value]
13. The change in length of the copper wire can be calculated using the formula:
ΔL = L₀αΔT
Where:
ΔL = change in length
L₀ = original length
α = coefficient of linear expansion
ΔT = change in temperature
Given:
- Original length of the wire (L₀) = 35.0 m
- Coefficient of linear expansion (α) = temperature dependent
- Change in temperature (ΔT) = 35.0°C - (-20.0°C) = 55.0°C
Calculate the change in length of the wire on a summer day when the temperature is 35.0°C.
14. The quantity of heat required to raise the temperature of 10g of ice from -10°C to steam at 110°C can be calculated by finding the heat required for each phase transition and for raising the temperature between the phases.
- Heat required to raise temperature of ice from -10°C to 0°C:
Q1 = m * c * ΔT
Q1 = 10g * 0.5 cal/g°C * 10°C
- Heat required for melting ice at 0°C:
Q2 = m * Lf
Q2 = 10g * 80 cal/g
- Heat required to raise the temperature of water from 0°C to 100°C:
Q3 = m * c * ΔT
Q3 = 10g * 1 cal/g°C * 100°C
- Heat required for vaporization at 100°C:
Q4 = m * Lv
Q4 = 10g * 540 cal/g
- Heat required to raise the temperature of steam from 100°C to 110°C:
Q5 = m * c * ΔT
Q5 = 10g * 0.5 cal/g°C * 10°C
Add all the calculated heats to find the total heat required.
15. To calculate how many kilograms of nitrogen boil away by the time the copper reaches 77.3K, we can use the heat exchanged equation:
m₁ * c₁ * ΔT₁ = m₂ * (ΔHv)₂ + m₂ * c₂ * ΔT₂
Where:
m₁ = mass of copper
c₁ = specific heat of copper
ΔT₁ = change in temperature for copper
m₂ = mass of nitrogen
ΔHv = latent heat of vaporization of nitrogen
c₂ = specific heat of nitrogen
ΔT₂ = change in temperature for nitrogen
Given:
- Mass of copper (m₁) = 1.00 kg
- Initial temperature of copper (T₁) = 20.0°C
- Final temperature of copper (T₂) = 77.3 K
- Latent heat of vaporization of nitrogen (ΔHv)₂ = 48.0 cal/g = 480 cal/kg
- Specific heat of copper (c₁) = 0.0920 cal/g°C
- Specific heat of nitrogen (c₂) = assuming it is negligible
Calculate the change in temperature for copper (ΔT₁) and nitrogen (ΔT₂) and solve for the mass of nitrogen that boils away.