A 1.41-kg aluminum pot contains 2.25 L of water. Both pot and water are initially at 17.5°C. How much heat must flow into the pot and the water to bring their temperature up to 92.7°C? Assume that the effect of water evaporation during the heating process can be neglected and that the temperature remains uniform throughout the pot and the water.

use the following values for the specific heats:
c_water=4.19 kJ/kg.K
c_aluminum=0.900 kJ/kg.K

To calculate the amount of heat that must flow into the pot and water to bring their temperature up to 92.7°C, we need to use the concept of heat transfer and the specific heat capacities of water (c_water = 4.19 kJ/kg.K) and aluminum (c_aluminum = 0.900 kJ/kg.K).

The formula for heat transfer is

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.

Let's go step by step to solve this problem:

1. Calculate the mass of water (m_water) in the pot using its density and volume:
Density of water (ρ_water) = 1 kg/L
m_water = ρ_water * V_water

Given:
V_water = 2.25 L

Substitute the values:
m_water = 1 kg/L * 2.25 L = 2.25 kg

2. Calculate the heat needed to raise the temperature of the water:
ΔT_water = T_final - T_initial

Given:
T_initial = 17.5°C
T_final = 92.7°C

Substitute the values:
ΔT_water = 92.7°C - 17.5°C = 75.2°C

Now, calculate the heat needed:
Q_water = m_water * c_water * ΔT_water

Substitute the values:
Q_water = 2.25 kg * 4.19 kJ/kg.K * 75.2°C

Calculate:
Q_water = 714.12 kJ

3. Calculate the heat needed to raise the temperature of the pot:
Now, we need to calculate the mass of the aluminum pot (m_pot).

Given:
m_pot = 1.41 kg

ΔT_pot = ΔT_water because they are in thermal contact.

Calculate the heat needed:
Q_pot = m_pot * c_aluminum * ΔT_pot

Substitute the values:
Q_pot = 1.41 kg * 0.900 kJ/kg.K * 75.2°C

Calculate:
Q_pot = 95.99 kJ

4. Calculate the total heat needed:
The total heat needed is the sum of the heat needed for the water and the pot.

Q_total = Q_water + Q_pot

Substitute the values:
Q_total = 714.12 kJ + 95.99 kJ

Calculate:
Q_total = 810.11 kJ

Therefore, to bring the pot and water to a temperature of 92.7°C, approximately 810.11 kJ of heat must flow into the system.