Question

Sarah is making bread. She measures 0.6 kg of hot water into a bowl. The water needs to be at a temperature of

exactly 42°C in order for the yeast to function properly, but right now it is at 40°C. What mass of additional
water at 49°C should she add to make it the correct temperature? Assume no heat is transferred to the bowl or
to the outside air. And please show your work

Answer 1

`\Delta m = 0.171\,kg`

Step-by-step explanation:

The process of water adding is described by the First Law of Thermodynamics:

`m_(w,o) \cdot h_(w,o) + \Delta m \cdot h_(w) = (m_(w,o) + \Delta m)\cdot h_(w,f)`

The amount of additional mass is:

`m_(w,o)\cdot h_(w,o) - m_(w,o)\cdot h_(w,f) = \Delta m\cdot (h_(w,f)-h_(w))`

`\Delta m = (m_(w,o)\cdot(h_(w,o)-h_(w,f)))/(h_(w,f)-h_(w))`

Given that water is incompressible, the equation can be further simplified:

`\Delta m = m_(w,o)\cdot (c_(p,w)\cdot (T_(w,o)-T_(w,f)))/(c_(p,w)\cdot (T_(w,f)-T_(w)))`

`\Delta m = m_(w,o)\cdot \left((T_(w,o)-T_(w,f))/(T_(w,f)-T_(w)) \right)`

`\Delta m = (0.6\,kg)\cdot \left((40 ^(\circ)C - 42^(\circ)C)/(42^(\circ)C-49^(\circ)C) \right)`

`\Delta m = 0.171\,kg`

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