27.2 g sample of ethylene glycol, a car radiator coolant, loses 685 J of heat. What was the initial temperature of ethylene glycol if the final temperature is 32.5°C (c of ethylene glycol = 2.42 J/gK)?
To find the initial temperature of ethylene glycol, we can use the formula for heat transfer:
Q = mcΔT
where Q is the heat transferred, m is the mass of the substance, c is the specific heat capacity, and ΔT is the change in temperature.
In this case, we are given the heat transferred (Q = 685 J), the mass of the ethylene glycol sample (m = 27.2 g), the final temperature (Tf = 32.5°C), and the specific heat capacity of ethylene glycol (c = 2.42 J/gK).
First, let's convert the final temperature to Kelvin (K):
Tf(K) = Tf°C + 273.15
Tf(K) = 32.5 + 273.15
Tf(K) = 305.65 K
Next, we can rearrange the formula to solve for the initial temperature (Ti):
Q = mcΔT
Ti = (Q / (mc)) + Tf
Substituting the given values:
Ti = (685 J / (27.2 g * 2.42 J/gK)) + 305.65 K
Now, let's calculate the initial temperature:
Ti = (685 J / 65.984 gK) + 305.65 K
Ti = 10.39 K + 305.65 K
Ti = 316.04 K
Therefore, the initial temperature of the ethylene glycol sample was approximately 316.04 K.