Question

Як зміниться внутрішня енергія одноатомного газу, якщо ізотермічно збільшити об'єм вдвічі?

Answer 1

Ответ:

Внутрішня енергія одноатомного газу не зміниться при ізотермічному збільшенні об'єму вдвічі. Це означає, що при постійній температурі, внутрішня енергія газу залишається незмінною, оскільки будь-яка зміна енергії компенсується зміною кінетичної енергії молекул газу.

Объяснение:

Answer 2

Change in Internal Energy of an Ideal Gas

When the volume of an ideal gas is increased isothermally (at constant temperature), the change in its internal energy depends on the type of process being considered. In this case, the process is an isothermal expansion where the volume of the gas is doubled.

During an isothermal expansion, the temperature of the gas remains constant. According to the ideal gas law, the pressure and volume of an ideal gas are inversely proportional when the temperature is constant. This relationship can be expressed as:

P₁V₁ = P₂V₂

Where: - P₁ and V₁ are the initial pressure and volume of the gas, respectively. - P₂ and V₂ are the final pressure and volume of the gas, respectively.

In this case, the volume of the gas is doubled, which means V₂ = 2V₁. Using this information, we can rewrite the equation as:

P₁V₁ = P₂(2V₁)

Simplifying the equation, we find:

P₁V₁ = 2P₂V₁

Dividing both sides of the equation by V₁, we get:

P₁ = 2P₂

This equation shows that the initial pressure of the gas is twice the final pressure.

Now, let's consider the change in internal energy (ΔU) of the gas during this process. The change in internal energy of an ideal gas is given by the equation:

ΔU = Q - W

Where: - ΔU is the change in internal energy. - Q is the heat added to the gas. - W is the work done by the gas.

In an isothermal process, the change in internal energy is zero because the temperature remains constant. Therefore, ΔU = 0.

Since ΔU = 0, the heat added to the gas (Q) must be equal to the work done by the gas (W). The work done by the gas during an expansion is given by the equation:

W = PΔV

Where: - P is the pressure of the gas. - ΔV is the change in volume of the gas.

In this case, the pressure of the gas changes from P₁ to P₂, and the volume of the gas changes from V₁ to 2V₁. Substituting these values into the equation, we get:

W = P₁(2V₁ - V₁) = P₁V₁

Since the work done by the gas is equal to the heat added to the gas, we can conclude that:

Q = P₁V₁

Therefore, the change in internal energy (ΔU) of the gas is zero, as there is no heat added or removed from the gas during an isothermal expansion.

To summarize, when the volume of an ideal gas is isothermally doubled, the change in its internal energy is zero.