Question

Тело нагревали нагревателем мощностью 600 Вт сначала на delta t, а потом еще на delta t, но уже нагревателем с вдвое большей мощностью. В результате весь процесс нагревания занял время T. Какая средняя мощность должна быть у нагревателя, чтобы сразу нагреть тело на 2 delta t за то же время T? ответ выразить в Вт, округлить до целых. Потерями принебречь .

Answer 1

Q1=P1*t1=c*T1 - тепло полученное при начальном нагреве
Q2=P2*t2=c*T2 - тепло полученное конечном нагреве
Q3=P3*t3=c*T3 - тепло, которое надо получить при нагреве неизвестным нагревателем
P1=P;
P2=2*P - мощность второго нагревателя больше в 2 раза
T1=T2=T - изменение температуры одинаково при двух нагревах
T3=Т1+Т2 = 2*T - изменение температуры при нагреве неизвестным нагревателем должно быть таким-же
P3 = ?
*****************
Q1=P*t1=c*T
Q2=(2*P)*t2=c*T
Q3=P3*(t1+t2)=c*(2*T)
******************
P*t1=c*T
2*P*t2=c*T
P3*(t1+t2)=c*(2*T)
***************
t1=c*T/P
t2=c*T/(2*P)
P3*(c*T/P + c*T/(2*P))=c*(2*T)
P3=2*P/(1/1+1/2)
P3=2*P/(3/2)
P3=4*P/3 = 4*600/3 Вт = 800 Вт

Answer 2

Problem Analysis

We are given that a body is initially heated by a heater with a power of 600 W for a time interval of delta t, and then it is further heated by a heater with twice the power for another time interval of delta t. The total time taken for the heating process is T. We need to find the average power that the heater should have in order to heat the body to 2 delta t in the same time interval T.

Solution

To solve this problem, we can use the concept of average power. The average power is given by the formula:

Average Power = Total Energy / Total Time

In this case, the total energy required to heat the body to 2 delta t is the same as the total energy required to heat the body to delta t twice. Therefore, we can write:

Total Energy = Energy required to heat the body to delta t + Energy required to heat the body to delta t

Let's assume the energy required to heat the body to delta t is E. Then the total energy required is 2E.

The total time taken for the heating process is T. Therefore, the average power can be calculated as:

Average Power = Total Energy / Total Time = 2E / T

Now, we need to find the value of E.

The energy required to heat a body can be calculated using the formula:

Energy = Power x Time

For the first heating process, the power is 600 W and the time is delta t. Therefore, the energy required to heat the body to delta t is:

E = 600 W x delta t

For the second heating process, the power is twice the initial power, which is 2 x 600 W = 1200 W, and the time is also delta t. Therefore, the energy required to heat the body to delta t is:

E = 1200 W x delta t

Since both heating processes require the same amount of energy, we can equate the two expressions for E:

600 W x delta t = 1200 W x delta t

Simplifying the equation, we find:

600 W = 1200 W

This equation is not possible, as it implies that 600 is equal to 1200. Therefore, there is no solution to this problem.

Conclusion

In order to heat the body to 2 delta t in the same time interval T, the average power required cannot be determined because the equation derived from the problem analysis does not have a valid solution.