Question

Most homes use a hot water tank to heat water. If 45.0 liters of water at 15.0°C enters a hot water tank where it is heated to 61.0°C, determine the amount of heat energy (J) needed to heat the water.

Answer 1

The hot water tank requires approximately 8.656 MJ of heat energy to heat 45.0 liters of water from 15.0°C to 61.0°C, calculated using the formula Q = m*c*ΔT with water's specific heat capacity of 4.184 J/g°C.

Step-by-step explanation:

To determine the amount of heat energy needed to heat 45.0 liters of water from 15.0°C to 61.0°C, we need to use the formula for calculating heat energy, Q = m*c*ΔT, where:

• m is the mass of the water,
• c is the specific heat capacity of water (4.184 J/g°C on average), and
• ΔT is the change in temperature.

First, convert the volume of water (45.0 L) to mass in grams (since 1 L of water is approximately 1 kg, 45.0 L is 45,000 g). Then, calculate the change in temperature (ΔT = 61.0°C - 15.0°C = 46.0°C).

Now, plug the values into the equation:

Q = (45,000 g) * (4.184 J/g°C) * (46.0°C)

Q = 8.65584 × 10^6 J, or 8655.84 kJ

Therefore, the hot water tank requires approximately 8.656 MJ (megajoules) of heat energy to heat the 45.0 liters of water from 15.0°C to 61.0°C.