. For an optimal gas, crafted by reversible extension under isothermal condition can be determined by utilizing the articulation

    \[w\text{ }=\text{ }\text{ }nRT\text{ }ln\text{ }Vf/Vi\]

An example containing 1.0 mol of an ideal gas is extended isothermally and reversibly to multiple times of its unique volume, in two separate tests. The extension is completed at 300 K and 600 K separately. Pick the right alternative. (I) Work done at 600 K is multiple times the work done at 300 K. (ii) Work done at 300 K is double the work done at 600 K. (iii) Work done at 600 K is double the work done at 300 K. (iv) ∆U = 0 in the two cases.
. For an optimal gas, crafted by reversible extension under isothermal condition can be determined by utilizing the articulation

    \[w\text{ }=\text{ }\text{ }nRT\text{ }ln\text{ }Vf/Vi\]

An example containing 1.0 mol of an ideal gas is extended isothermally and reversibly to multiple times of its unique volume, in two separate tests. The extension is completed at 300 K and 600 K separately. Pick the right alternative. (I) Work done at 600 K is multiple times the work done at 300 K. (ii) Work done at 300 K is double the work done at 600 K. (iii) Work done at 600 K is double the work done at 300 K. (iv) ∆U = 0 in the two cases.

solution:

 

Alternative (iii) and (iv) are the appropriate responses.

work done at 600 K is double the work done at 300 K. Since each case includes isothermal extension of an optimal gas, there is no adjustment of interior energy, i.e., 

    \[U\text{ }=\text{ }0\]

.