1 mol of an ideal gas is kept in a cylinder, fitted with a piston, at the position A, at 18°C. If the piston is moved to position B, keeping the temperature unchanged, then ‘x’ L atm work is done in this reversible process.

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Solution

Q.

Consider the figure provided.

1 mol of an ideal gas is kept in a cylinder, fitted with a piston, at the position A, at 18°C. If the piston is moved to position B, keeping the temperature unchanged, then ‘x’ L atm work is done in this reversible process.

x = _____ L atm. (nearest integer)

[Given: Absolute temperature = °C + 273.15,
R = 0.08206 L atm ${mol}^{- 1}$ $K^{- 1}$ ] [2024]

Ans.
(55)

Work done by gas in isothermal reversible expansion is:

$w = - 2.303 n R T \log_{10} \frac{V_{2}}{V_{1}}$

$w = - 2.303 \times 1 \times 0.08206 \times 291.15 \times \log_{10} \frac{100}{10} atmL$

$w = - 2.303 \times 1 \times 0.08206 \times 291.15 \times \log_{10} 10 atmL$

$w = - 55.023 atmL \approx - 55 atmL$

Work done by system = +55 atmL

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