Help With A Chemistry Problem Please

Question

Answer 1

You want to use the equation q=mc(Delta T), where m is the mass, c the specific heat capacity, and Delta T is the change in heat (T1 - T2). Since this is a closed system, in which the total energy remains constant, we know that the energy lost by the iron as it cools down, will be equal to the energy gained by the water, as it is heated up by the hot metal. So qMetal = qWater. However, one of these q's is going to be negative since the mass in question is losing heat (an exothermic process), so ACTUALLY, qMetal = - qWater. Most of the time you are either given or expected to know the specific heat capacity of water, which is 4.184 J/(gC), so I will take that as given in my solution. When the system reaches equilibrium, both water and metal will have the same temperature, so there is only one T2. I'll let you keep track of significant figures (assuming your prof wants you to) as well as units as it is hard to keep writing them out.

qM = 72.4gMetal * 0.449 J/(gC)(100 - T2)

qW = 100 gWater * 4.184 J/(gC)(10 - T2)

We cannot solve for either qM or qW unless we know T2 (which is actually the answer to c)), however we already know that qM=-qW, so we can write

72.4gMetal * 0.449 J/(gC)(100 - T2) = -(100 gWater * 4.184 J/(gC)(10 - T2)) and solve for T2

First we multiply through to get

72.4*0.449*100 - 72.4 *0.449*T2 = - (100*4.184*10 - 100*4.184*T2)

Then we get all the terms with T2 on one side, and all the other terms on the other side

-72.4*0.449T2 - 100*4.184T2 = -100*4.184*10 - 72.4*0.449*100

-32.5T2 - 418.4T2 = -4184 - 3250.76

-450.9 T2 = 7434.76

T2 = 7434.76/450.9. This is the answer to c)

Now that we have T2, we can plug it into the above equations for qM and qW to get answers for a) and b) respectively.