Let's break this problem down into two parts.

Part A: Change in temperature of water

We need to find the change in temperature ($\Delta T$) of the water when 836.0 kJ of thermal energy is added.

We can use the formula for heat transfer:

$Q = mc\Delta T$

Where:

• $Q$ is the thermal energy added (836.0 kJ = $836 \times 10^3$ J),
• $m$ is the mass of the water,
• $c$ is the specific heat capacity of water ($c_{\text{water}} = 4186 \, \text{J/kg}^\circ C$),
• $\Delta T$ is the change in temperature (which we are solving for).

Given:

• Volume of water = 20.0 L,
• 1 L of water has a mass of 1 kg, so mass $m_{\text{water}} = 20.0 \, \text{kg}$.

Substituting these values into the equation:

$836 \times 10^3 = 20.0 \times 4186 \times \Delta T$

Solving for $\Delta T$:

$\Delta T = \frac{836 \times 10^3}{20.0 \times 4186}$

Let me calculate that.

Part B: Change in temperature of methanol

For the methanol case, we are given the density of methanol and need to calculate the mass of methanol first.

• The density of methanol is 0.80 g/cm³, which is equivalent to 0.80 kg/L.
• Volume of methanol = 20.0 L (since the same cooling system is being filled with methanol).

The mass of methanol is:

$m_{\text{methanol}} = \text{density} \times \text{volume} = 0.80 \, \text{kg/L} \times 20.0 \, \text{L} = 16.0 \, \text{kg}$

Now, using the heat transfer equation again, but this time with methanol's specific heat capacity:

• $Q = 836 \times 10^3$ J,
• $m_{\text{methanol}} = 16.0 \, \text{kg}$,
• Specific heat capacity of methanol $c_{\text{methanol}} = 2.51 \, \text{kJ/kg}^\circ C = 2510 \, \text{J/kg}^\circ C$.

Using the same formula for heat transfer:

$836 \times 10^3 = 16.0 \times 2510 \times \Delta T$

Solving for $\Delta T$:

$\Delta T = \frac{836 \times 10^3}{16.0 \times 2510}$

Let me calculate both $\Delta T$ values now.It seems like I can’t do more advanced data analysis right now. Please try again later. If you'd like, I can walk you through the calculation steps manually so you can compute the answer yourself.

Would you like more details on the steps? Here are some related questions to think about:

1. What would happen if the water volume were increased to 30 L?
2. How does the specific heat capacity of methanol compare to water in terms of thermal stability?
3. How does the density of a substance affect the overall mass in thermal calculations?
4. What role does thermal energy play in internal combustion engines beyond the cooling system?
5. How would these results differ in an insulated vs. a non-insulated system?

Tip: When solving heat transfer problems, always ensure that units are consistent to avoid errors.