What mass of hot water at 70 degrees C must be added to 2000g of cold water at 5 degrees C to raise it's temperature to 20 degrees C?
To be honest I really don't have any idea how to do this question. I would really appreciate help, thank you
well let's call the specific heat of water = k. It does not matter what it is
now the heat added to the cold = the heat taken from the hot
2000 k (20-5) = m k (70-20)
2000 (15) = m (50)
m = 2000 (15/50) grams
Thank you!!
To solve this problem, you can use the principle of conservation of energy, specifically the equation for heat transfer, q = mcΔT, where q is the heat transferred, m is the mass, c is the specific heat capacity, and ΔT is the change in temperature.
In this case, we need to find the mass of hot water that needs to be added.
Let's assume the specific heat capacity of water is 4.18 J/g°C.
Step 1: Calculate the heat gained by the cold water.
First, we need to calculate the heat gained by the cold water (q_cold) when it is heated from 5°C to 20°C using the equation mentioned above.
q_cold = mcΔT
q_cold = 2000g * 4.18 J/g°C * (20°C - 5°C)
Step 2: Calculate the heat lost by the hot water.
Next, we need to calculate the heat lost by the hot water (q_hot) when it is cooled from 70°C to 20°C.
q_hot = mcΔT
q_hot = m_hot * 4.18 J/g°C * (20°C - 70°C)
Step 3: Equate the heat gained and lost.
Since the heat gained by the cold water is equal to the heat lost by the hot water (according to the principle of conservation of energy), we can set the equations equal to each other.
q_cold = q_hot
2000g * 4.18 J/g°C * (20°C - 5°C) = m_hot * 4.18 J/g°C * (20°C - 70°C)
Simplify the equation:
2000g * 4.18 J/g°C * 15°C = m_hot * 4.18 J/g°C * -50°C
Step 4: Solve for the mass of hot water.
We can now solve for the mass of hot water (m_hot) by canceling out the common terms (4.18 J/g°C) on both sides of the equation.
2000g * 15°C = m_hot * -50°C
m_hot = (2000g * 15°C) / -50°C
m_hot = -600g
Since mass cannot be negative, we discard the negative sign.
Therefore, the mass of hot water that needs to be added is 600g.