Hello, Anya,
I will need to make three assumptions in the calculations:
1. May I assume that when you state 201.5 of water that you meant to say 201.5 kg? I will assume that 201.5kg is correct.
2. The 2122 of energy is 2.122 kJ, not 2122 kJ or 2122 calories.
3. Is the value of 4.184 is in units of kJ/kg*K? I assume this is correct.
The specific heat number (in this case) tells us how much heat is changed per 1 kg of substance per 1 degree K change in temperature. The units are important here, because Cp can be found in a variety of units involving moles, calories, etc.
The energy (Q) lost by the water is -2.122 kJ (kilojoules). The "-" sign shows that the energy is lost from the water. A "+" would mean that energy is gained by the water.
The formula to use is Energy (Q) = Cp*M*(T2-T1), where
M is the mass in kg (since that is the unit in Cp)
T2 and T1 are the final and initial temperatures, in Kelvin, and
Cp is the specific heat of the water.
In English, this equation says the energy change (Q) in a system is equal to its mass M, times the specific heat Cp, times the temperature change (T2 - T1).
Since we want to find the change in temperature, lets rearrange the equation:
(T2 - T1) =Q/(Cp*M)
Plugging in Q, Cp and M, we get:
(T2 - T1) = -2.122kJ/ (4.186kJ/kg/(K *201.5kg))
T2-T1 = -2.517 K
The temperature dropped 2.517 K. This is the same value in C. In 4 sig figs, the answer is the temperature changed by -2.517 C. We aren’t given a starting temperature. Whatever it was, it is cooler by 2.517 C now.
This would change if any of my assumptions was incorrect.
I hope this helps,
Bob
