What would be the final temperature of a mixture of 80 g of 25 c water and 150 g of water at 75 c?

c•m1• (t-25) = c•m2• (75-t)

80t - 80•25 =150•75- 150t
230t= 13250
t=57.6°

To find the final temperature of the mixture, we can use the principle of heat transfer, which states that the heat gained by the cooler substance is equal to the heat lost by the hotter substance. We can calculate this using the equation:

Q = mcΔT

Where:
Q = heat gained/lost
m = mass of the substance
c = specific heat capacity
ΔT = change in temperature

First, let's calculate the heat lost by the hot water:

Q_lost = m_hot * c_water * ΔT_hot

Where:
m_hot = mass of hot water
c_water = specific heat capacity of water (4.18 J/g°C)
ΔT_hot = change in temperature (final temperature - initial temperature)

m_hot = 150 g
c_water = 4.18 J/g°C
ΔT_hot = (final temperature - initial temperature) = (final temperature - 75°C)

Next, let's calculate the heat gained by the cold water:

Q_gained = m_cold * c_water * ΔT_cold

Where:
m_cold = mass of cold water
c_water = specific heat capacity of water (4.18 J/g°C)
ΔT_cold = change in temperature (final temperature - initial temperature)

m_cold = 80 g
c_water = 4.18 J/g°C
ΔT_cold = (final temperature - initial temperature) = (final temperature - 25°C)

Since the heat lost by the hot water equals the heat gained by the cold water, we can set them equal to each other:

Q_lost = Q_gained

m_hot * c_water * ΔT_hot = m_cold * c_water * ΔT_cold

Now, we can substitute the given values into the equation and solve for the final temperature:

150 g * 4.18 J/g°C * (final temperature - 75°C) = 80 g * 4.18 J/g°C * (final temperature - 25°C)

Now, we can simplify the equation:

627 J/°C * (final temperature - 75°C) = 334.4 J/°C * (final temperature - 25°C)

627(final temperature - 75) = 334.4(final temperature - 25)

627final temperature - 47025 = 334.4final temperature - 8360

627final temperature - 334.4final temperature = 47025 - 8360

292.6final temperature = 38665

final temperature ≈ 38665 / 292.6

final temperature ≈ 132.1°C

Therefore, the final temperature of the mixture would be approximately 132.1°C.