1. Tardigrade
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  3. Chemistry
  4. At a temperature of 298K,1mol of a monoatomic ideal gas is expanded from the State (.1.) to State (.2.) as shown in the graph: <img class=img-fluid question-image alt=Question src=https://cdn.tardigrade.in/q/nta/c-oiptuq8yiovkmclm.jpg /> . Find out the work done for the expansion of gas from the State (.1.) to State (.2.) at 298K ?

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Q. At a temperature of $298K,1mol$ of a monoatomic ideal gas is expanded from the State $\left(\right.1\left.\right)$ to State $\left(\right.2\left.\right)$ as shown in the graph:
Question .
Find out the work done for the expansion of gas from the State $\left(\right.1\left.\right)$ to State $\left(\right.2\left.\right)$ at $298K$ ?

NTA AbhyasNTA Abhyas 2020

Solution:

The given statement represents that the process is carried out in infinite steps.
Hence, it is an isothermal reversible expansion of the ideal gas from pressure 2.0 atm to 1.0 atm at 298 K.
W = -2.303 nRT log $\frac{\text{p}_{1}}{\text{p}_{2}}$
W = -2.303 x 1 x 8.314 x 298 x (0.3010) $\left(\because \frac{\left(\text{p}\right)_{1}}{\left(\text{p}\right)_{2}} = \frac{2}{1}\right)$
W = -1717.46 J