Question

During the summer after your first year at Carnegie Mellon, you are lucky enough to get a job making coffee at Starbucks, but you tell your parents and friends that you have secured a lucrative position as a "java engineer." An eccentric chemistry professor (not mentioning any names) stops in every day and orders 250ml of Sumatran coffee at precisely 75.0°C. You then need to add enough milk at 7.00°C to drop the temperature of the coffee, initially at 85.0°C, to the ordered temperature. Required:Calculate the amount of milk (in ml) you must add to reach this temperature.

Answer 1

The answer is "36.76 ml "

Step-by-step explanation:

Answer 2

The answer is "36.76 ml "

Step-by-step explanation:

In the given question, Its basic understanding to also be hired seems to be that coffee heat = heat that the milk absorbs

The following relationship defines heat:

`\to q = m C_(p)( T_2 - T_1)`

Its updated equation is:

`\to q_(\ coffee) = - q_\ milk} \\\\ \to m_(\ milk) C_(p) (T_2 - T_1)_(\ coffee) = - m_( \ milk) C_(p) (T_2 - T_1)_(\ milk) ..........(a)`

The following information is provided to you as per the question:

1) Milk and coffee have the same heat power

2) Difference in coffee temperature is:

`\to (T_2 - T_1)_(\ coffee) = 75.0^(\circ) \ \ C-85.0^(\circ) \ \ C`

`= -10.0 ^(\circ) \ \ C`

3) The difference in milk temperature:

`\to (T_2 - T_1)_( \ milk) = 75.0^(\circ) \ \ C- 7.0^(\circ) \ \ C`

`= 68.0 ^(\circ) \ \ C`

4) Milk and coffee density are equal therefore, weight and volume are equal and have same ratio, that can be shown as follows:

`\to \ Density (\rho) =( \ Mass (m))/( \ Volume (V)) \\\\\to m= V * \rho \\\\`

`\to m_(\ coffee) * (T_2 - T_1)_( \ coffee)= -m_(\ milk) * (T_2 - T_1)_(milk) \\\\\to V_(\ coffee) * \rho_(\ coffee) * (T_2 - T_1)_(\ coffee) = - V_(\ milk) * \rho_(\ milk) * (T_2 - T_1)_(\ milk) \\\\\to V_(\ coffee) * (T_2 - T_1)_(\ coffee) = - V_(\ milk) * (T_2 - T_1)_(\ milk).............(b)`

by replace the equation values (b) for calculating milk volumes as shown as follows:

`\to V_(\ coffee) * (T_2 - T_1)_(\ coffee) = - V_(\ milk) * (T_2 - T_1)_(\ milk)\\\\\to 250 ml * (-10 .0^(\circ) \ \ C) = - V_(\ milk) * (68.0^(\circ) \ \ C)\\\\\to V_(\ milk)= (250 ml * (-10 .0^(\circ) \ \ C) )/(- (68.0^(\circ) \ \ C))`

`= 36.76 \ ml`