Question

В кружку с водой при температуре 10°С и массой 330 Г положили металлический стержень массой 1 кг.Найдите начальную температуру стержня,если вода нагрелась до 60°С (С воды=4200 Дж/к2×°С; С стержня =693 Дж/к2×°С)

Answer 1

T₁=10°C                                  уравнение теплового баланса:
m₁=330 г=0,33 кг                       Q₁=Q₂:
m₂=1 кг                             c₁m₁(t₂-t₁)=c₂m₂(t-t₂); выразим (t),
t₂=60°C                            c₁m₁(t₂-t₁)=c₂m₂t-c₂m₂t₂;
c₁=4200 Дж/кг°С             c₁m₁(t₂-₁)+c₂m₂t₂=c₂m₂t; ⇒
c₂=693 Дж/кг°С                ⇒ t= {c₁m₁(t₂-t₁)+c₂m₂t₂}/c₂m₂;
_______________               t={4200*0,33*50+693*1*60}/693*1=160°C;
t-?                                  Ответ: t=160°C.

Answer 2

Calculation of Initial Temperature of the Metal Rod

To find the initial temperature of the metal rod, we can use the principle of conservation of energy. The heat gained by the water is equal to the heat lost by the metal rod.

The heat gained by the water can be calculated using the formula:

Q_water = m_water * C_water * ΔT_water

Where: - Q_water is the heat gained by the water - m_water is the mass of the water (330 g) - C_water is the specific heat capacity of water (4200 J/(kg·°C)) - ΔT_water is the change in temperature of the water (60°C - 10°C = 50°C)

Substituting the given values into the formula, we have:

Q_water = 0.33 kg * 4200 J/(kg·°C) * 50°C

Calculating the value of Q_water gives us:

Q_water = 69300 J

Now, we can equate the heat gained by the water to the heat lost by the metal rod:

Q_water = Q_rod

The heat lost by the metal rod can be calculated using the formula:

Q_rod = m_rod * C_rod * ΔT_rod

Where: - Q_rod is the heat lost by the metal rod - m_rod is the mass of the metal rod (1 kg) - C_rod is the specific heat capacity of the metal rod (693 J/(kg·°C)) - ΔT_rod is the change in temperature of the metal rod (initial temperature - final temperature)

Substituting the given values and rearranging the equation, we have:

Q_rod = 1 kg * 693 J/(kg·°C) * (initial temperature - 60°C)

Now, we can equate the two equations:

Q_water = Q_rod

69300 J = 1 kg * 693 J/(kg·°C) * (initial temperature - 60°C)

Simplifying the equation, we have:

initial temperature - 60°C = 69300 J / (1 kg * 693 J/(kg·°C))

initial temperature - 60°C = 100°C

Finally, solving for the initial temperature, we get:

initial temperature = 100°C + 60°C

initial temperature = 160°C

Therefore, the initial temperature of the metal rod is 160°C.