Water mixing

We have 520 ml of hot water and 640 ml of water at 48°C. What is the temperature of approximately hot water when the resulting mixture has a temperature of 65°C?

Correct answer:

t₁ =  85.9231 °C

Step-by-step explanation:

$$\begin{gathered} V_1=520\text{ ml } \\ {V}_2=640\text{ ml } \\ {t}_2=48\text{ ° } \\ t=65\text{ ° } \\ Q=m\cdot c\cdot (t-t_0) \\ m=\rho V \\ Q=\rho V\cdot c\cdot (t-t_0) \\ {Q}_1+Q_2=Q \\ \rho \cdot V_1\cdot c\cdot (t_1-t_0)+\rho \cdot V_2\cdot c\cdot (t_2-t_0)=\rho \cdot (V_1+V_2)\cdot c\cdot (t-t_0) \\ {V}_1\cdot (t_1-t_0)+V_2\cdot (t_2-t_0)=(V_1+V_2)\cdot (t-t_0) \\ {V}_1\cdot t_1+V_2\cdot t_2=t\cdot (V_1+V_2) \\ 520\cdot t_1+640\cdot 48=65\cdot (520+640) \\ 520t_1=44680 \\ {t}_1={\displaystyle \frac{1117}{13}}\doteq 85.923077=85.9231\text{°C} \end{gathered}$$

Try another example

Related math problems and questions:

• There
  There is 5 l of water with a temperature of 20°C in the bucket. We add 3 liters of hot water. The resulting temperature will be 30°C. What was the temperature of the hot water?
• The bath
  The bath has water with a volume of 220 l and a temperature of 65°C. Determine the mass m₂ of water at 15°C to be poured so that the resulting temperature of the water in the bath is 40°C. We neglect the heat exchange between water and the environment. T
• Mixing water
  We should fill the 30-liter container with water at 60 degrees Celsius. How many liters of water 80 degrees C hot, and how many liters of water 20 degrees Celsius warm we have to mix?
• The bath
  Dad poured 50 liters of water at 60°C into the tub. How much cold water must be added at 10°C to obtain a bath that has a temperature of 40°C?
• The pool
  The pool has a volume of 40 m³, and the water temperature is 20 °C. How much water at 100 °C should we pour into the pool to increase the water temperature by 5 °C?
• Water temperatures
  To 25 liters of water at 50 °C we add 15 liters of water at a different temperature. How many °C should the water be colder than 50 °C so that 40 liters of the water obtained has a temperature 42.5 °C?
• The aluminum
  The aluminum object with a weight of 0.80 kg and a temperature of 250°C was placed in the water with a weight of 1.6 kg and a temperature of 23°C. What is the system temperature after reaching equilibrium? We assume that the heat exchange occurred only be
• Latent heat
  How much heat is needed to take from 100 g of water at 20°C to cool to ice at -18°C? Mass heat capacity c (ice) = 21kJ/kg / °C; c (water) = 4.19 KJ/kg / °C and the mass group heat of solidification of water is l = 334kJ/kg
• Water
  Mix 68 l of water with a temperature of 87 °C, 17 l warm of 42 °C, and 55 l water of 50 °C. What is the temperature of the mixed water immediately after mixing?
• Water mixing
  There are 5 liters of water at 75°C in the pot, how much water at 10°C do we have to add to the resulting temperature of 55°C?
• Petra
  Petra likes to bathe in a bathtub with a water temperature of 38 degrees. She turned on the hot water set at 70 degrees and left for a moment. Before she returned, 40 liters of water flowed into the tub. How much water with a temperature of 22 degrees mus
• Bath
  In the bath is 30 liters of hot water. Then added 36 liters of cold water at temperature of 19 °C decreased temperature of water to 41 °C. What was the initial temperature of the hot water?
• Milk mixing
  You have 12 liters of milk with a temperature of 20°C. How much milk at 80°C do you have to add to have milk at 30°C?
• Thermometer
  Immerse a thermometer with a heat capacity of 2.0 J. K-1 in water weighing 67.0 grams. Before immersion in water, the thermometer showed a temperature of 17.8 degrees Celsius. After reaching equilibrium, the temperature is 32.4 degrees. What was the water
• Coffee
  In-stock are three kinds of branded coffee prices: I. Kind. .. .. .205 Kc/kg II. Kind. .. .. .274 Kc/kg III. Kind. .. .. 168 Kc/kg Mixing these three species in the ratio 8:5:6 create a mixture. What will be the price of 100 grams of this mixture?
• Heat transfer
  We placed a lead object weighing 0.4 kg and 250°C in 0.4 L water. What was the initial temperature of water t2 if the object's temperature and the water after reaching equilibrium was 35°C? We assume that the heat exchange occurred only between the lead o
• Alcohol 2
  Two types of alcohol one 63% and second 75% give 20 liters of 69% alcohol. How many liters of each type are in the mixture?