A 26.5 g sample of ethylene glycol, a car radiator coolant, loses 675 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)?

Please help me, I don't even know where to begin!!

q = mass e.g. x specific heat e.g. x (Tfinal-Tinitial).

Since the coolant LOST (released) 67 J, be sure to set q = -675

Oh, radiator coolant, the unsung hero of car overheating situations! Well, let's cool things down and calculate the initial temperature of ethylene glycol, shall we?

First, we need to find the heat energy lost by the ethylene glycol using the formula:

Q = mcΔT

Where:
Q is the heat energy lost (675 J),
m is the mass of the ethylene glycol (26.5 g),
c is the specific heat capacity of ethylene glycol (2.42 J/gK), and
ΔT is the change in temperature (final temperature - initial temperature).

So, we have:

675 J = 26.5 g * 2.42 J/gK * (32.5°C - T)

Now, let's solve this equation for T, the initial temperature:

675 J = 64.13 gJ/K * (32.5°C - T)

675 J = 2070.325 J - 64.13 gJ/K * T

64.13 gJ/K * T = 2070.325 J - 675 J

64.13 gJ/K * T = 1395.325 J

T = 1395.325 J / 64.13 gJ/K

T ≈ 21.75°C

So, the initial temperature of the ethylene glycol was about 21.75°C (or just around room temperature). Keep cool, my friend!

To determine the initial temperature of ethylene glycol, we can use the formula for heat transfer:

Q = mcΔT

Where:
Q = heat transfer (in joules)
m = mass of ethylene glycol (in grams)
c = specific heat capacity of ethylene glycol (in J/gK)
ΔT = change in temperature (in °C)

In this problem, we are given the mass of ethylene glycol (26.5 g), the heat transfer (675 J), the final temperature (32.5°C), and the specific heat capacity of ethylene glycol (2.42 J/gK).

First, we need to determine the change in temperature (ΔT):

ΔT = final temperature - initial temperature
ΔT = 32.5°C - initial temperature

Now, substituting the given values into the formula for heat transfer:

675 J = (26.5 g)(2.42 J/gK)(32.5°C - initial temperature)

Next, we can solve for the initial temperature by rearranging the equation:

(26.5 g)(2.42 J/gK)(32.5°C - initial temperature) = 675 J

Now, divide both sides of the equation by (26.5 g)(2.42 J/gK) to isolate the term (32.5°C - initial temperature):

(32.5°C - initial temperature) = 675 J / (26.5 g)(2.42 J/gK)

Finally, solve for the initial temperature by subtracting the value obtained on the right side from 32.5°C:

initial temperature = 32.5°C - (675 J / (26.5 g)(2.42 J/gK))

Simplifying this expression will give you the answer for the initial temperature of ethylene glycol.

To find the initial temperature of the ethylene glycol, we can use the formula for heat transfer:

q = m * c * ΔT

where:
q is the heat transferred
m is the mass of the substance
c is the specific heat capacity of the substance
ΔT is the change in temperature

In this case, we are given:
q = -675 J (negative sign indicates heat loss)
m = 26.5 g
c = 2.42 J/gK
ΔT = (final temperature - initial temperature)

We need to rearrange the formula to solve for the initial temperature (Ti). The rearranged formula becomes:

ΔT = q / (m * c)

Let's calculate the change in temperature first:

ΔT = 32.5°C - Ti

Now substitute the given values into the rearranged formula:

32.5°C - Ti = -675 J / (26.5 g * 2.42 J/gK)

To simplify this equation, convert the temperatures to Kelvin by adding 273.15:

(305.65 K - Ti K) = -675 J / (26.5 g * 2.42 J/gK)

Now, rearrange the equation to solve for Ti:

Ti = 305.65 K + (675 J / (26.5 g * 2.42 J/gK))

Now, calculate the value of Ti:

Ti ≈ 305.65 K + 10.27 K

Ti ≈ 315.92 K

Therefore, the initial temperature of the ethylene glycol is approximately 315.92 K.