Question

Consider a piston filled with 3 mols of an ideal gas, kept at a constant temperature 290 K. We slowly compress the gas starting at 2 m3 and ending at 1 m3. How much work do we need to do on the gas to perform this operation

Answer 1

Answer: $-5013.65\ J$

Explanation:

Given

No of moles $n=3$

Temperature $T=290\ K$

Initial volume $V_1=2\ m^3$

Final volume $V_2=1\ m^3$

Work done in constant temperature process is

$W=nRT\ln \left(\dfrac{V_2}{V_1}\right)$

Insert the values

$\Rightarrow W=3\times 8.314\times 290\ln \left (\dfrac{1}{2}\right)\\\\\Rightarrow W=-870\times 8.314\times \ln (2)\\\Rightarrow W=-5013.65\ J$