Question

Определите установившуюся температуру при смешивании воды массой 200 г и температурой 40º , воды массой 30 г и температурой 10º .

Answer 1

Дано: 
m1=200 г
t1=40°C
m2=30 г
t2=10°C
Найти t-?

Решение:
При смешивании теплой(будем называть теплой воду, температура которой 40) и холодной (соответственно холодная вода с температурой 10), теплая вода отдает теплоту равную Q1, а холодная вода поглащает теплоту равную Q2. Т.к.  энергия никуда не девается Q1=Q2. 

Q1=c*m1(t1-t);
Q2=c*m2(t-t2).

c*m(t1-t)=c*m(t-t2); (с, удельная теплоемкость, принимает одинаковые значение и потому сокращается )
Получаем: 
m1*(t1-t)=m2*(t-t2);
Выражаем отсюда t : 
t=(m1*t1+m2*t2)/(m1+m2)=(200*40+30*10)/(200+30)=36,1°C

Answer 2

Calculation of the Final Temperature

To determine the final temperature when mixing water with different masses and temperatures, we can use the principle of conservation of energy. The total heat gained by one body is equal to the total heat lost by the other body.

Let's denote the mass of the first body as m1, the initial temperature of the first body as t1, the mass of the second body as m2, and the initial temperature of the second body as t2.

The formula to calculate the final temperature tf is:

tf = (m1 * t1 + m2 * t2) / (m1 + m2)

Now let's apply this formula to the given values:

- The first body has a mass of 200 g and an initial temperature of 40ºC. - The second body has a mass of 30 g and an initial temperature of 10ºC.

Using the formula, we can calculate the final temperature as follows:

tf = (200 g * 40ºC + 30 g * 10ºC) / (200 g + 30 g)

Calculating this expression gives us the final temperature.

Calculation:

tf = (200 g * 40ºC + 30 g * 10ºC) / (200 g + 30 g)

tf = (8000 gºC + 300 gºC) / 230 g

tf = 8300 gºC / 230 g

tf ≈ 36.09ºC

Therefore, the final temperature after mixing the water with masses of 200 g and 30 g, and initial temperatures of 40ºC and 10ºC respectively, is approximately 36.09ºC.

Please note that the above calculation assumes that there is no heat loss to the surroundings and that the specific heat capacity of water remains constant throughout the process.