1. Tardigrade
  2. Question
  3. Chemistry
  4. A gas present in a cylinder fitted with a frictionless piston expands against a constant pressure of 1 atm from a volume of 2 litre to a volume of 6 litre. In doing so, it absorbs 800 J heat from surroundings. Determine increase in internal energy of process.

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Q. A gas present in a cylinder fitted with a frictionless piston expands against a constant pressure of $1$ atm from a volume of $2$ litre to a volume of 6 litre. In doing so, it absorbs $800\, J$ heat from surroundings. Determine increase in internal energy of process.

Thermodynamics

Solution:

Since, work is done against constant pressure and thus, irreversible.
Given, $\Delta V= \left(6 -2\right) = 4L; P= 1$ atm
$\therefore W = - 1\times 4L -atm $$= - \frac{1 \times4 \times1.987}{0.0821}$ cal
(since $0.0821 L-atm = 1.987$ cal)
$=-96.81$ cal $= - 96.81 \times4.184\, J \left(\because 1 cal = 4.184 J\right)$
$ = - 405.05 \,J$
Now from $I^{st}$ law of thermodynamics
$q =\Delta U -W$
$ 800 = \Delta U + 405.05$
$\therefore \Delta U = 395\,J$