An intrepid explorer takes 400 g of ice from the cold Siberian environment, where the temperature is –40 degrees and places it in a kettle inside his mobile laboratory. The ice melts and he heats the water to +40 degrees. What is the total amount of heat absorbed by the explorer’s sample of H2O?

q1 = heat absorbed to raise T from -40 to zero.

q1 = mass ice x specific heat ice x (Tfinal-Tinitial)

q2 = heat absorbed to melt ice at zero to form liquid water at zero..
q2 = mass ice x heat fusion.

q3 = heat absorbed to raise T liquid water from zero to +40C.
q3 = mass water x specific heat water x (Tfinal-Tinitial).

Total q = q1 + q2 + q3.

To calculate the total amount of heat absorbed by the explorer's sample of H2O, we need to consider two steps: the heat absorbed during the melting of the ice and the heat absorbed during the heating of the water.

1. Heat absorbed during the melting of the ice:
The heat required to melt a substance can be calculated using the formula:
Q = m * L
where Q is the heat absorbed, m is the mass of the substance, and L is the specific heat of fusion.

Given:
mass of ice (m) = 400 grams = 0.4 kg (since 1 kg = 1000 grams)
specific heat of fusion (L) = 334,000 J/kg

Using the formula, we can calculate the heat absorbed during the melting of the ice:
Q1 = 0.4 kg * 334,000 J/kg = 133,600 J

2. Heat absorbed during the heating of water:
The heat required to increase the temperature of a substance can be calculated using the formula:
Q = m * c * ΔT
where Q is the heat absorbed, m is the mass of the substance, c is the specific heat capacity, and ΔT is the change in temperature.

Given:
mass of water (m) = 0.4 kg (since it was originally ice)
specific heat capacity of water (c) = 4,186 J/kg·°C (approximately)
change in temperature (ΔT) = 40°C - 0°C = 40°C

Using the formula, we can calculate the heat absorbed during the heating of the water:
Q2 = 0.4 kg * 4,186 J/kg·°C * 40°C
Q2 = 66,976 J

Finally, to find the total amount of heat absorbed by the explorer's sample of H2O, we add the results from both steps:
Total heat absorbed = Q1 + Q2
Total heat absorbed = 133,600 J + 66,976 J
Total heat absorbed ≈ 200,576 J

Therefore, the total amount of heat absorbed by the explorer's sample of H2O is approximately 200,576 J.