Sir please answer this, Calculate the amount of work done when one mole of an ideal gas present in a bulb of 5 litres capacity at one atmosphere pressure is allowed to enter into an evacuated bulb of 50 litres capacity.

To calculate the work done when one mole of an ideal gas expands from a smaller bulb to a larger evacuated bulb, we can use the formula for work done during an isothermal expansion. In this case, since the gas is expanding into a vacuum, the work done can be simplified because there is no opposing pressure. Let's break this down step by step.

Understanding the Scenario

We have one mole of an ideal gas initially contained in a bulb with a volume of 5 liters at a pressure of 1 atmosphere. The gas is then allowed to expand into a second bulb with a volume of 50 liters, which is initially evacuated (meaning it has no gas in it).

Key Concepts

• Ideal Gas Law: The behavior of the gas can be described by the ideal gas law, which states that PV = nRT, where P is pressure, V is volume, n is the number of moles, R is the ideal gas constant, and T is temperature.
• Work Done: In thermodynamics, the work done by a gas during expansion against an external pressure is given by W = -P_ext ΔV, where P_ext is the external pressure and ΔV is the change in volume.

Calculating the Work Done

In this scenario, since the gas is expanding into a vacuum, the external pressure (P_ext) is effectively zero. Therefore, the work done by the gas can be calculated as follows:

Step 1: Determine the Initial and Final Volumes

The initial volume (V_i) is 5 liters, and the final volume (V_f) after expansion is 50 liters. The change in volume (ΔV) can be calculated as:

ΔV = V_f - V_i = 50 L - 5 L = 45 L

Step 2: Calculate Work Done

Since the gas is expanding into a vacuum, the work done (W) is:

W = -P_ext ΔV = -0 × 45 L = 0

Conclusion

In this case, the work done by the gas during the expansion into the evacuated bulb is zero. This is because there is no opposing pressure to do work against. The gas expands freely without exerting any force on an external environment. Thus, the final answer is:

Work Done = 0 Joules

This example illustrates an important concept in thermodynamics: when a gas expands into a vacuum, it does not perform work on the surroundings, as there is no resistance to its expansion. If you have any further questions or need clarification on any part of this process, feel free to ask!