Answer to Question #101171 in Physical Chemistry for GHOST

Question

Draw and explain the steps involved in cannot cycle.

Answer 1

Following are the four processes of Carnot cycle:

In (a), the process is reversible isothermal gas expansion. In this process, the amount of heat absorbed by the ideal gas is q_in from the heat source which is at a temperature of T_h. The gas expands and does work on the surroundings.

In (b), the process is reversible adiabatic gas expansion. Here, the system is thermally insulated and the gas continues to expand and work is done on the surroundings. Now the temperature is lower, T_I.

In (c), the process is reversible isothermal gas compression process. Here, the heat loss, q_out occurs when the surroundings do the work at temperature T_I.

In (d), the process is reversible adiabatic gas compression. Again the system is thermally insulated. The temperature again rise back to T_h as the surrounding continue to do their work on the gas.

Step 1:

Isothermal expansion: The gas is taken from P₁, V₁, T₁ to P₂, V₂ ,T₂. Heat Q₁ is absorbed from the reservoir at temperature T₁. Since the expansion is isothermal, the total change in internal energy is zero and the heat absorbed by the gas is equal to the work done by the gas on the environment, which is given as:

W₁→₂=Q₁=μ×R×T₁×ln(v₂/v₁)

Step 2:

Adiabatic expansion: The gas expands adiabatically from P₂, V₂, T₁ to P₃, V₃, T₂.

Here work done by the gas is given by:

W₂→₃={μR/(γ−1)}*(T₁−T₂)

Step 3:

Isothermal compression: The gas is compressed isothermally from the state (P₃, V₃, T₂) to (P₄, V₄, T₂).

Here, the work done on the gas by the environment is given by:

W₃→₄=μRT₂ln(v₃/v₄)

Step 4:

Adiabatic compression: The gas is compressed adiabatically from the state (P₄, V₄, T₂) to (P₁, V₁, T₁).

Here, the work done on the gas by the environment is given by:

W₄→₁={μR/(γ−1)}*(T₁−T₂)