Question

Сколько кубиков льда при температуре -8 С надо бросить в литровую банку с водой при температуре 38 С, чтобы охладить воду до 18 С, если объём каждого кубика 4 см3?

Answer 1

Лед нагрев до 0
Q1=C1m1(0-(-8))=2100*8*m1=16800m1
Q2=лm1=33000m1 лед тает
Q3=cm1(18-0)=75600m1 - нагрев до 18С
Q4=cm2(38-18)=4200*1*20=84000Дж - охлаждение 1литр воды(1 л=1кг)
Q4=Q1+Q2+Q3
84000=m1(16800+330000 +75600)
m1=pv=84000/(16800+330000 +75600)
V=m1/p,где р плотность воды
N=v/v1=(84/(16800+330000 +75600))/4*10^-6
v1=4*10^-6 м куб. объем одного кубика льда

Answer 2

Calculation of the Number of Ice Cubes Needed to Cool Water

To calculate the number of ice cubes needed to cool water, we need to consider the initial temperature of the water, the desired final temperature, and the volume of each ice cube.

Given: - Initial temperature of the water: -8°C - Final temperature of the water: 18°C - Volume of each ice cube: 4 cm³

To calculate the number of ice cubes needed, we can follow these steps:

1. Calculate the temperature difference between the initial and final temperatures: Final Temperature - Initial Temperature = 18°C - (-8°C) = 26°C

2. Calculate the total heat energy that needs to be removed from the water: Heat Energy = Mass of Water × Specific Heat Capacity × Temperature Difference

Since we are dealing with a fixed volume of water (1 liter), we can assume its mass is equal to its density: Mass of Water = Volume of Water × Density of Water

The density of water is approximately 1 gram/cm³, and 1 liter is equal to 1000 cm³: Mass of Water = 1000 cm³ × 1 g/cm³ = 1000 g

The specific heat capacity of water is approximately 4.18 J/g°C: Heat Energy = 1000 g × 4.18 J/g°C × 26°C = 108,680 J

3. Calculate the heat energy absorbed by each ice cube: Heat Energy per Ice Cube = Volume of Ice Cube × Density of Ice × Specific Heat Capacity of Ice × Temperature Difference

The density of ice is approximately 0.92 g/cm³: Heat Energy per Ice Cube = 4 cm³ × 0.92 g/cm³ × 2.09 J/g°C × 26°C = 199.712 J

4. Calculate the number of ice cubes needed: Number of Ice Cubes = Total Heat Energy / Heat Energy per Ice Cube

Number of Ice Cubes = 108,680 J / 199.712 J ≈ 544.2

Therefore, approximately 544 ice cubes are needed to cool the water from -8°C to 18°C, assuming each ice cube has a volume of 4 cm³.

Please note that this calculation assumes ideal conditions and does not account for factors such as heat transfer losses or the melting of ice cubes during the cooling process.