Question

Какую массу стали , взятой при температуре плавления можно расплавить с помощью нагревательного элемента с кпд 40%, если при напряжении 100В по нему проходит ток 10А.Время плавления полчаса.

Answer 1

К-во тепла, которое выделит нагревательный элемент за полчаса:
 Q=U*I*t=100*10*1800*0,4=720 000(Дж);
q=84кДЖ/кг   -  удельная теплота плавления стали;
m=Q/q=720 000/84 000=8,6(кг);
Ответ:  можно расплавить m=8,6кг стали.

Answer 2

Calculating the Mass of Steel that can be Melted

To calculate the mass of steel that can be melted using a heating element with 40% efficiency, a voltage of 100V, a current of 10A, and a melting time of half an hour, we can use the formula:

Power (P) = Voltage (V) × Current (I)

The power can then be used to calculate the energy consumed, which can be used to find the mass of steel melted.

Calculating Power

Using the given voltage and current, we can calculate the power:

P = V × I P = 100V × 10A P = 1000W

Calculating Energy Consumed

The energy consumed can be calculated using the formula:

Energy (E) = Power (P) × Time (t)

Given that the time is half an hour (0.5 hours), we can calculate the energy consumed:

E = P × t E = 1000W × 0.5h E = 500Wh

Calculating the Mass of Steel Melted

To find the mass of steel melted, we can use the energy consumed and the efficiency of the heating element.

Given that the efficiency is 40%, the actual energy used for melting is:

Actual Energy = Efficiency × Energy Consumed Actual Energy = 0.40 × 500Wh Actual Energy = 200Wh

Using the Specific Heat Capacity of Steel

The specific heat capacity of steel is approximately 460 J/kg°C. We can convert the energy consumed to joules and then use the specific heat capacity to find the mass of steel melted.

Converting Watt-hours to Joules

1 watt-hour (Wh) = 3600 joules (J)

Energy in Joules = Energy in Watt-hours × 3600 Energy in Joules = 200Wh × 3600 Energy in Joules = 720000J

Calculating the Mass of Steel Melted

Using the specific heat capacity of steel, we can calculate the mass of steel melted:

Energy = Mass × Specific Heat Capacity × Temperature Change

Given that the temperature change for melting steel is approximately 1500°C, we can rearrange the formula to solve for the mass:

Mass = Energy / (Specific Heat Capacity × Temperature Change) Mass = 720000J / (460 J/kg°C × 1500°C) Mass ≈ 320 kg

Conclusion

Therefore, with a heating element of 40% efficiency, a voltage of 100V, a current of 10A, and a melting time of half an hour, it is possible to melt approximately 320 kilograms of steel.