Find the heat absorbed by an ideal gas (in kJ ) when it follows the graph (given below) during an isothermal expansion $[ln 2 = 0.7]$ [Take : 1 litre-bar $= 0.1 kJ]$

Question

Find the heat absorbed by an ideal gas (in kJ ) when it follows the graph (given below) during an isothermal expansion [ ln 2 = 0.7 ] [Take : 1 litre-bar = 0.1 kJ ]

TestHub · Accepted Answer

Explanation: Find the heat absorbed by an ideal gas (in kJ ) when it follows the graph during an isothermal expansion.

Concept: This question is based on isothermal process.

Solution:

From the graph, at initial state A: $P_{1} = 100 ba r$ and $V_{1} = 1 L$ .

For an isothermal process, first find the final volume $V_{2}$ at point B:

$100 ba r \times 1 L = 50 ba r \times V_{2} ⟹ V_{2} = 2 L$ .

Now, calculate the work done using the relationship $n RT = P_{1} V_{1}$ :

$w = - P_{1} V_{1} ln (\frac{V _{2}}{V _{1}})$

$w = - (100 ba r \cdot 1 L) \times ln (\frac{2 L}{1 L}) = - 100 ln 2 ba r \cdot L$

Substitute the given values (ln⁡ 2 = 0.7 and 1bar⋅L = 0.1 kJ):

$w = - 100 \times 0.7 = - 70 ba r . L$

$w (ink J) = - 70 \times 0.1 = - 7 k J$

Applying the First Law of Thermodynamics ( $Δ U = q + w = 0$ for an isothermal process):

$q = - w = - (- 7 k J) = 7 k J$

Final Answer: 7

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