Gas Laws

The problem requires determining the ratio of the work done by a monatomic gas to the heat absorbed by it as it undergoes a change from state A to state B shown in the PV diagram. Let's analyze this step-by-step.

1. The given graph shows the volume (V) vs temperature (T) for a monatomic gas. We can assume an ideal gas where the state equation is given by .
2. First Law of Thermodynamics: The change in internal energy of the gas is given by: where is the heat absorbed and is the work done by the gas.
3. Monatomic Gas Internal Energy Change: The change in internal energy for a monatomic ideal gas is: Here, is the change in temperature.
4. Work Done (W): For a process at constant pressure, work done can be expressed as: due to the ideal gas law.
5. Ratio Calculation: The problem asks for the ratio of work done by the gas to the heat absorbed: Using the first law, rearrange to express : Therefore, the ratio becomes:
6. The correct option is hence found to be: , which matches the given correct answer.