A sample of oxygen gas expands its volume from 3 litre to 5 litre against a constant pressure of 3.6 atm. If the work done during expansion be used to heat 10 mole of water initially present at 290 K, its final temperature (in K) is _______ (Rounding to nearest integer) (Specific heat capacity of water $= 4 J k^{- 1} g^{- 1}, 1 L atm = 100 J$ )

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answer is 291.

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Detailed Solution

Work done in expansion $= P \times V = 3 \times (5 - 3) = 6 l i t - a t m$

we have 1 litre atm = 101.3 J

work done $= 6 \times 1.013 J = 607.8 J$

Let $Δ T$ be the change in temperature of water.

$∴ P Δ V = m \times s \times Δ T$

$607.8 = 180 \times 4.184 \times Δ T$

$Δ T = 0.81 K$

$T_{f} = T_{1} + Δ T = 290.9 K$

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