Question

The calorie is a unit of energy defined as the amount of energy needed to raise 1 g of water by 1°C. a. How many calories are required to bring a pot of water at 1°C to a boil? The pot is full to the brim, with diameter 20 cm and depth 20 cm. The density of water is 1000 kg/m3. b. If we consider that D for the pot is 20 cm, approximately how much more energy is needed to heat a hot tub with D = 2 m? How many calories is that?

Answer 1

a. Calories required = 622710 calories

b. Energy = 1000 times much energy

Calories = 622710000 calories

Explanation:

Given:

h = Depth of pot = 20cm = 0.2m

Diameter of pot = 20cm = 0.2m

r = ½ *diameter = ½ * 0.2

r = 0.1m

Density = 1000kg/m³

Water temperature = 1°C

a.

First, we calculate the volume of the water(pot)

V = Volume = πr²h

V = 22/7 * 0.1² * 0.2

V = 0.044/7

V = 0.00629m³

M = Mass of water = Volume * Density

M = 0.00629m³ * 1000kg/m³

M = 6.29kg

M = 6.29 * 1000 grams

M = 6290g

The water is at 1°C, so it needs to gain 99°C to reach boiling point

So, Calories = 99 * 6290

Calories required = 622710 calories

b.

If we consider that D for the pot is 20 cm, approximately how much more energy is needed to heat a hot tub with D = 2 m? How many calories is that?

Depth of pot = 20cm

Depth of pot = 0.2m

Depth of hot tube = 2m

Energy is directly proportional to D³

Since the depth of hot the is 10 times greater than that of the pot

It'll require 10³ much more energy

Energy = 10³

Energy = 1000 times much energy

Calories required = 622710 * 1000

Calories = 622710000 calories