Question

3. Двухатомный идеальный газ, занимающий при давлении Р. 0,3 МПа объем V = 4 л, расширяется до объема V, = 6 л. При этом устанавливается давление 0,1 МПа. Определить работу газа и изменение его внутренней энергии при а) адиабатном и б) изохориче- ском процессах. Помогите пожалуйста.

Answer 1

Ответ:

1) A = 1500 Дж; ΔU = –1500 Дж; 2) A = 0; ΔU = –1500 Дж

Answer 2

Calculation of Work and Change in Internal Energy

To calculate the work and change in internal energy for the given process, we need to consider two scenarios: adiabatic and isochoric processes.

# Adiabatic Process

In an adiabatic process, there is no heat exchange with the surroundings. Therefore, the change in internal energy is equal to the work done on or by the gas.

The work done by the gas can be calculated using the formula:

W = P_initial * V_initial^γ - P_final * V_final^γ / (γ - 1)

Where: - W is the work done by the gas - P_initial is the initial pressure - V_initial is the initial volume - P_final is the final pressure - V_final is the final volume - γ is the heat capacity ratio (specific heat capacity at constant pressure divided by specific heat capacity at constant volume)

The change in internal energy (ΔU) is equal to the work done by the gas.

# Isochoric Process

In an isochoric process, the volume remains constant. Therefore, no work is done by or on the gas. The change in internal energy is equal to the heat added or removed from the gas.

Since the volume remains constant, the work done is zero (W = 0). The change in internal energy (ΔU) is equal to the heat added or removed from the gas.

Now, let's calculate the work and change in internal energy for both scenarios.

# Adiabatic Process:

Given: - Initial pressure (P_initial) = 0.3 MPa - Initial volume (V_initial) = 4 L - Final volume (V_final) = 6 L - Final pressure (P_final) = 0.1 MPa

Using the formula mentioned above, we can calculate the work done by the gas:

W = (P_initial * V_initial^γ - P_final * V_final^γ) / (γ - 1)

To calculate the change in internal energy, we can use the formula:

ΔU = W

# Isochoric Process:

Given: - Initial pressure (P_initial) = 0.3 MPa - Initial volume (V_initial) = 4 L - Final volume (V_final) = 6 L - Final pressure (P_final) = 0.1 MPa

Since the volume remains constant, the work done is zero (W = 0). The change in internal energy (ΔU) is equal to the heat added or removed from the gas.

Now, let's calculate the change in internal energy for the isochoric process:

ΔU = Q

Note: The formulas mentioned above assume that the gas behaves ideally and follows the ideal gas law.