find the final equilibirum temperature when 10.0 g of milk at 10.0degC is added to 1.60*10^2 g of coffee with a temperatrure of 90.0degC. Assume the specific heats of coffee and milk are the same as for water (Cp,w=4.19J/g*degC) and disregard the heat capacity of the container
massmilk*cmilk*(Tf-10)+masscoffee(ccoffee)(Tf-90)=0
please show me in simple steps how to solve for Tf
thanks a lot
massmilk*cmilk*(Tf-10)+masscoffee(ccoffee)(Tf-90)=0
divide through by specific heat, it goes away.
10*(Tf-10)+160(Tf-90)=0
Tf(10+160)-100-160*90=0
Tf= (14400/170)
so Tf is 84.70?
the Tf is about 85.3°C because it's actually Tf = 14,500/170
To find the final equilibrium temperature (Tf) when adding milk and coffee, we can use the principle of conservation of energy. The heat lost by one substance is equal to the heat gained by the other substance.
Step 1: Determine the mass of milk (mmilk) and coffee (mcoffee):
Given:
- Mass of milk (mmilk) = 10.0 g
- Mass of coffee (mcoffee) = 1.60 × 10^2 g
Step 2: Calculate the specific heat capacities (c) of milk and coffee:
Assuming the specific heat capacities of milk and coffee are the same as water, c = 4.19 J/g°C.
Step 3: Write the heat transfer equation:
The heat lost by the milk = Heat gained by the coffee.
massmilk * cmilk * (Tf - initial temperature of milk) + masscoffee * ccoffee * (Tf - initial temperature of coffee) = 0
Substituting the given values:
(10.0 g) * (4.19 J/g°C) * (Tf - 10.0°C) + (1.60 × 10^2 g) * (4.19 J/g°C) * (Tf - 90.0°C) = 0
Step 4: Simplify the equation:
- Multiply the terms within the parentheses.
- Combine like terms.
(41.9 J/°C * g * Tf - 419 J/°C * g) + (668 J/°C * g * Tf - 6012 J/°C * g) = 0
(41.9 J/°C * g * Tf + 668 J/°C * g * Tf) - 419 J/°C * g - 6012 J/°C * g = 0
(709.9 J/°C * g * Tf) - 6422 J/°C * g = 0
Step 5: Rearrange the equation to solve for Tf:
Move the constant terms to the opposite side of the equation.
709.9 J/°C * g * Tf = 6422 J/°C * g
Step 6: Solve for Tf:
Divide both sides of the equation by (709.9 J/°C * g) to isolate Tf.
Tf = (6422 J/°C * g) / (709.9 J/°C * g)
Step 7: Perform the calculation:
Divide the numerator by the denominator to find the value of Tf.
Tf ≈ 9.06°C
Therefore, the final equilibrium temperature is approximately 9.06°C.