Question

Peter is heating water on the stove to boil eggs for a picnic. If it takes 800 kcal to heat his vat of water from 20◦C to 100◦C, how much water did he have?

Answer 1

Step-by-step explanation:

The amount of heat energy required to raise the temperature of a given mass of a substance is given by the specific heat capacity of the substance. For water, the specific heat capacity is approximately 1 calorie/gram °C or 4.184 joule/gram °C.

To determine the mass of water Peter heated, we can use the following formula:

Q = m * c * ΔT

where Q is the amount of heat energy, m is the mass of the substance, c is the specific heat capacity, and ΔT is the change in temperature.

In this case, Q is given as 800 kcal, or 800,000 calories, and the change in temperature, ΔT, is 100°C - 20°C = 80°C.

Using the specific heat capacity of water, c = 1 calorie/gram °C, we can rearrange the formula to solve for the mass, m:

m = Q / (c * ΔT)

Substituting the given values, we get:

m = 800,000 calories / (1 calorie/gram °C * 80°C)

m = 800,000 grams

m = 800 kg

Therefore, Peter heated 800 kg, or 800 liters, of water.