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You have 750 g of water at 10°C in a large insulated beaker. How much boiling water at 100°C must you add to this beaker so that the final
temperature of the mixture will be 75°C? For water, c = 4.19 x 103 J/(kg • K).
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Respuesta :

grujan50

Answer:

Correct answer:  m₂ = 1,950 g

Explanation:

When mixing the liquid, in this case water, at different temperatures, the warmer liquid will cool and the cooler will warm up until their temperatures equalize.

The amount of heat that the second fluid (water) releases is equal to the amount of heat that the first fluid (water) receives in this spontaneous process.

Q₁ = Q₂

Q₁ = m₁ c (t - t₁)    and Q₂ = m₂ c (t₂ - t)  

where are they:  m₁ = 750 g, t₁ = 10°C, t₂ = 100°C, t = 75°C, m₂ = ?

m₁ c (t - t₁)  = m₂ c (t₂ - t) \ : c

Since water is the liquid in question, it has the same specific heat capacity. Therefore, we will divide both sides of the equation by c and get:

m₁ (t - t₁)  = m₂ (t₂ - t) =>  m₂ = m₁ (t - t₁) / (t₂ - t) =>

m₂ = 750 · (75 - 10) / (100 - 75) => m₂ = 750 · 65 / 25 = 1,950 g

m₂ = 1,950 g

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snehashish65

The required amount of boiling water is 1950 g.

Given data:

The mass of water is, m₁ = 750 g = 0.75 kg.

The temperature of water is, t₁ = 10°C.

The temperature of boiling water is, t₂ = 100°C.

The final temperature of mixture is, t = 75°C.

The specific heat of water is, [tex]c=4.19 \times 10^{3} \;\rm J/kg.K[/tex].

When mixing the liquid, in this case water, at different temperatures, the warmer liquid will cool and the cooler will warm up until their temperatures equalize.

The amount of heat that the second fluid (water) releases is equal to the amount of heat that the first fluid (water) receives in this spontaneous process.

Q₁ = Q₂

Q₁ = m₁ c (t - t₁)    and  Q₂ = m₂ c (t₂ - t)  

Then solving as,

m₁ c (t - t₁)  = m₂ c (t₂ - t)

m₁ (t - t₁)  = m₂ (t₂ - t)

m₂ = m₁ (t - t₁) / (t₂ - t)

m₂ = 750 · (75 - 10) / (100 - 75)

m₂ = 750 · 65 / 25 = 1,950 g

m₂ = 1,950 g

Thus, we can conclude that the required amount of boiling water is 1950 g.

Learn more about the thermal equilibrium here:

https://brainly.com/question/24401513

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