InterviewSolution
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InterviewSolution
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(a) What is the free expansion? Determine work done in case of free expansion of an ideal gas. (b) 4.0 mol of ideal gas at 2 atm and 25°C expands isothermally to 2 times of its original volume against the external pressure of 1 atm. Calculate work done. If the same gas expands isothermally in a reversible manner, then what will be the value of work done? |
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Answer» (a) When a gas expands under vacuum i.e. no external pressure work on it (Pex = 0), its expansion is called free expansion. \(\because\) Pex = 0 \(\therefore\) W = 0 in case of free expansion of an ideal gas [\(\because\) W= -Pex (V2 - V1) = 0] It means no work is done (b) Given n = 4 moles P = 2 atm T = 25 + 273 = 298 K Pex = 1 atm \(\therefore\) W = -Pex(Vf - Vi) Now, initial (Vi) =\(\frac{nRT}{P}\) = \(\frac{4\times0.082\times298}{2}\) = 48.87 L \(\because\) Volume becomes 2 times of its original volume. \(\therefore\) Final volume (Vf = 48.87 × 2 = 97.74 L) \(\therefore\) W = −1(97.74 − 48.87) = −1(48.87) = −48.87 J For isothermal reversible expansion of ideal gas Wrev = -2.303 nRT log\(\frac{V_f}{V_i}\) = −2.303 × 4 × 8.314 × 298 log\(\big(\frac{97.74}{48.87}\big)\) = −2.303 × 4 × 8.314 × 298 × 0.3010 = −6869.84 J |
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