An ideal gas expands isothermally from to at 300 K against a constant pressure of . The work done on the gas is [2019]

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Solution

Q.
An ideal gas expands isothermally from $10^{- 3} m^{3}$ to $10^{- 2} m^{3}$ at 300 K against a constant pressure of $10^{5}$ $N$ $m^{- 2}$ . The work done on the gas is [2019]

1 +270 kJ

2 -900 J

3 +900 kJ

4 -900 kJ

Ans.
(2)

$w = - P d V = - P (V_{2} - V_{1})$

$= - 10^{5} {Nm}^{- 2} (10^{- 2} - 10^{- 3}) m^{3} = - 10^{5} {Nm}^{- 2} (9 \times 10^{- 3}) m^{3}$

$= - 9 \times 10^{2} Nm = - 900$ $J$ $(∵ 1 J = 1 Nm)$

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