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Question

Water (2570 gg ) is heated until it just begins to boil. If the water absorbs 4.85×105 JJ of heat in the process, what was the initial temperature of the water?

Answer 1

q = mC∆T

q = heat = 4.85x105 J

m = mass = 2570 g

C = specific heat = 4.184 J/gº

∆T = change in temperature = ?

Solving for ∆T:

∆T = q/(m)(C) = 4.85x105 J/(2570 g)(4.184 J/gº)

∆T = 45.1º

Since the normal boiling point for water is 100ºC, the initial temperature of the water must have been 100 - 45.1 = 54.9º

Answer 2

Hello, Anya,

I will need to make two assumptions in the calculations:

1. May I assume that when you state 2570 gg of water that you meant to say 2570 g? I'll assume that 2570 g is correct, and convert it to 2.570 kg for the problem (divide by 1,000 to go from g to kg).
2. I'll assume when you wrote 4.85×105 JJ, that you meant to say 4.85×10^5 J, instead. Converted to kJ, this becomes 4.85x10^2 kJ.

The specific heat (Cp) of water is 4.186 kJ/kg*K, as you pointed out.

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. Be aware that the same information can be expressed in other units, such as kJ/mole/C, calories/g/K, etc. Check the units and convert where necessary. In this case we can use it with the one caveat it uses the Kelvin temperature scale. [It would not make a difference if it were K or C in this case, because we are looking for the temperature DIFFERENCE, and the resulting value would would be the same, whether it is C or K.

For reference, the conversion to K is:

K = C +273

The energy (Q) absorbed by the water is +4.85x10^2 kJ (kilojoules). The "+" sign shows that the energy is going into the system A "-" would mean that energy is being released.

The formula we want to use is Energy (Q) = CpM(T2-T1), where

M is the mass in kg (since that's what unit is 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 the change in temperature, lets rearrange the equation:

(T2 - T1) =Q/(Cp*M)

Plugging in Q, Cp and M, we get:

(T2 - T1) = 4.85x10^2kJ/[ (4.186kJ/kg/K) *(2.57kg)]

The calculation results in the number 45.1K.

(T2 - T1) = 45.1K

So the temperature increased by 45.1K. The increase in C would be the same, 45.1C.

I hope this helps,

Bob