Final answer:
The question pertains to the work done by a dilute gas during a quasi-static isothermal expansion at a constant temperature of 310 K. It involves concepts such as isothermal expansion, the ideal gas law, and the first law of thermodynamics.
Step-by-step explanation:
Work Done by an Expanding Gas at Constant Temperature
When a dilute gas expands quasi-statically from 0.7 to 3.5 L at a constant temperature of 310 K, doing 290 J of work, the process described is an isothermal expansion. In such a thermodynamic process, the work done by the gas can be described using the formula W = nRT ln(V2/V1), where W is the work done, n is the number of moles of gas, R is the universal gas constant, T is the temperature, and V1 and V2 are the initial and final volumes, respectively. Keeping the temperature constant implies that all the work done by the gas comes at the expense of heat absorbed from the surroundings, according to the first law of thermodynamics. To calculate the moles of gas or further analyze this process, additional information such as the initial pressure or the gas constant is required.
The relevant principles involved here include isothermal expansion, the ideal gas law, and the first law of thermodynamics. All these are foundational concepts in physics, specifically, in the branch of thermodynamics. Knowing these can help solve problems related to heat, work, and internal energy changes in gases under various conditions.