When 155 mL of water at 26 C is mixed with 75 mL of water at 85 C, what is the final temperature? (Assume that no heat is lost to the surroundings; d of water 1.00 g/mL.)

Question

When 155 mL of water at 26 C is mixed with 75 mL of water at 85 C, what is the final temperature? (Assume that no heat is lost to the surroundings; d of water  1.00 g/mL.)

anonymous · Answer

Someone please help, I really don't know where to begin or how to solve this. :( Even just an equation will do.

wach · Answer

I'm not that familiar with this exact calculation, so excuse me if I'm wrong. 
The equation for this should be : 

( Volume1 * Temp1) + (Volume2 * Temp2) / (Volume1 + Volume2) = Final temp

noelgreco · Answer

The amount of heat a substance gains or loses is governed by the following formula:

$$Q=mc \Delta T$$

Where Q is the heat lost or gained, m is the mass in kg, c is the specific heat of the substance (c-1.00 for water), and deltaT is the change in temperature.  Since the heat gained by the cold water is = to the heat lost by the warm water the two Qs can are equal.  Thertefore:

$$m _{c} \Delta T _{c }=m _{w}\Delta T _{w}$$

The c and w subscripts are for the cold and warm water.

Since both waters are at the same final temperature:

$$m _{c}(T _{f}-26)=m _{w}(85-T _{f})$$  where T sub f is the final temp for both masses of water.  The expressions in the parentheses were switched because you always want a positive delta T.

anonymous · Answer

Thank you so much!