Question

На скільки відрізняються внутрішні енергії 10 кг води та 10 кг пари за температури 100 °С?​

Answer 1

Дано:

m=10кг

t¹=0 C°

t²=100C°

Answer 2

Calculation of the Difference in Internal Energy

To calculate the difference in internal energy between 10 kg of water and 10 kg of steam at a temperature of 100 °C, we need to consider the specific heat capacities and the phase changes involved.

Water: The specific heat capacity of water is approximately 4.18 J/g°C. Since we have 10 kg of water, we can calculate the energy required to raise its temperature from 0 °C to 100 °C using the formula:

Q = m * c * ΔT

Where: - Q is the energy (in Joules) - m is the mass of the substance (in grams) - c is the specific heat capacity (in J/g°C) - ΔT is the change in temperature (in °C)

For water, the change in temperature is 100 °C - 0 °C = 100 °C.

Steam: When water reaches its boiling point and undergoes a phase change from liquid to gas, it absorbs additional energy known as the latent heat of vaporization. The latent heat of vaporization for water is approximately 2260 J/g.

To calculate the energy required to convert 10 kg of water at 100 °C to steam at 100 °C, we need to consider two steps: 1. Raising the temperature of water from 100 °C to its boiling point (100 °C). 2. Vaporizing the water at its boiling point.

For step 1, we use the same formula as before, but with the mass of water being 10 kg (10,000 grams) and the specific heat capacity of water.

For step 2, we calculate the energy required to vaporize the water using the formula:

Q = m * L

Where: - Q is the energy (in Joules) - m is the mass of the substance (in grams) - L is the latent heat of vaporization (in J/g)

For steam, the mass is still 10 kg (10,000 grams), and the latent heat of vaporization is 2260 J/g.

Calculation Results

Using the above calculations, we can determine the difference in internal energy between 10 kg of water and 10 kg of steam at 100 °C.

The energy required to raise the temperature of 10 kg of water from 0 °C to 100 °C is calculated as follows: Q_water = m * c * ΔT = 10,000 g * 4.18 J/g°C * 100 °C = 4,180,000 J

The energy required to vaporize 10 kg of water at 100 °C is calculated as follows: Q_vaporization = m * L = 10,000 g * 2260 J/g = 22,600,000 J

Therefore, the total difference in internal energy between 10 kg of water and 10 kg of steam at 100 °C is the sum of the energy required for raising the temperature and the energy required for vaporization: Total difference = Q_water + Q_vaporization = 4,180,000 J + 22,600,000 J = 26,780,000 J

Please note that the above calculations assume ideal conditions and do not take into account any losses or inefficiencies.