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With the advent of the financial crisis, how to save money for families has become the hottest topic. In fact, there are things worth discovering in life. For example, now, convenient and fast electric kettles have generally entered our lives, greatly shortening the time of boiling water, and are deeply favored by us. Therefore, there are various styles and models of electric kettles on the market now, but how to choose the right electric kettle for your family?
Analysis and investigation
Example: So I studied the rapid heating and power consumption of electric kettle boiling water. I found that the electric kettle is marked as shown in the figure, as shown in Figure 2. Through my investigation, the service life of these two types of electrical appliances is three years. The market price of rapid heating is 250 yuan, and the market price of electric kettle is 270 yuan (0.5 yuan per kilowatt hour).
Volume of water (ml)
Volume of water (ml)
Current (Ampere)
Time (seconds)
Immersed electric heater
1750
220
4.5
700
electric kettle
3500
220
/
850
Q (1) When the daily water consumption of a family is 3500ml, which one should be more economical and energy-saving?
(2) When a family's daily boiling water is 7000ml, which is more economical and energy-saving?
Solution: (1) Let the power consumption be W and the cost be S.
Rapid heating:
w 1 = UIT = 220v * 4.5A * 700s *(3500ml)/( 1750ml)= 1386000j = 0.385kwh
S 1 3 years electricity consumption =0.385 kwh *365 days *3*0.5 yuan =2 10.7875 yuan.
S 1 total =2 10.7875+250=460.7875 yuan.
For electric kettle:
w2 = PT = 850s * 1.5 * 1000 w = 1275000j = 17/48kwh
S2 Three-year electricity fee = 17/48 kWh *365 days *3*0.5 yuan = 193.906 yuan.
S2 total = 193.906+270=463.906 yuan.
Because 463.906 yuan > 460.7875 yuan, it is more economical and energy-saving to buy quickly.
(2) For rapid heating:
w 1 = UIT = 220v * 4.5A * 700s *(7000ml)/( 1750ml)= 2772000j = 0.77kwh
S 1 3 years electricity consumption =0.77 kwh *365 days *3*0.5 yuan = 42 1.575 yuan.
S 1 total = 421.575+250 = 671.575 yuan.
For electric kettle:
w2 = PT = 1500 w * 850s *(7000ml)/(3500ml)= 2550000j = 17/24k wh
S2 Three-year electricity fee = 17/24 kWh *365 days *3*0.5 yuan = 387.85438+025 yuan.
S2 total = 387.8125+270 = 657.438+025 yuan.
Because 657.8 125 yuan
summary
By comparing the two data, it is more economical to use heat quickly when the daily household water consumption is 3500ml, and it is more economical to use electric kettle when the daily household water consumption is 7000ml. It can be seen that the types and models of products that should be selected are different according to the daily water consumption of families. We can buy a practical and energy-saving water heater according to the actual situation at home.
abstract
The above calculation and comparison are only based on individual examples. The power models of various products on the market are also different. In order to make every family buy according to their own actual situation, I want to introduce a universal formula.
Settings:
Volume of water (ml)
Power (Watts)
time
Immersed electric heater
V 1
P 1
T 1
electric kettle
V2
P2
T2
Let's assume that the daily water consumption of a family is xml, the market price of a quick heating is A yuan, the market price of an electric kettle is B yuan, and the service life is 3 years (0.5 yuan per kilowatt hour).
while
[(x/v 1)*p 1*t 1]/(3.6* 10^6)*3*365*0.5+a<； [(x/v2)*p2*t2]/(3.6* 10^6)*3*365*0.5+b
Simplify:
[(x/v 1)*p 1*t 1*547.5-(x/v2)*p2*t2*547.5]/(3.6* 10^6)<； (b-a)
x[(p 1 * T2/v 1)-(P2 * T2/V2)]& lt； (480000/73)*(b-a)
Buying quickly is more economical and energy-saving.
Conversely, when x [(p1* t2/v1)-(p2 * t2/v2)] >; (480000/73)*(b-a)
Buying an electric water heater is more economical and energy-saving.
After the above research, do you see the knowledge in the purchase? Hurry up and investigate your daily water consumption to see if your hot water kettle is the most economical.
Reflection on problem solving
How to buy home appliances is more economical? This is a question worth discussing. We should proceed from our own actual situation and choose the one that suits us best in combination with the market. From the above topics, we can understand that mathematics can change life and even improve it. For example, we can discuss how to save energy and reduce emissions, how to calculate carefully for ourselves and so on. There is mathematics everywhere in life. While enjoying life, we should also pay attention to the mathematics around us, apply what we have learned and seek more tips for ourselves and others.