One mole of an ideal gas is initially at 0°C and 1 atm pressure. If it absorbs 1000 cal heat during a reversible isothermal expansion, what will be its final volume?

Question

One mole of an ideal gas is initially at 0°C and 1 atm pressure. If it absorbs 1000 cal heat during a reversible isothermal expansion, what will be its final volume? (A) 102.5 litre (B) 242.5 litre (C) 22.4 litre (D) 121.25 litre

Tardigrade Admin · Accepted Answer

Since the gas is under S.T.P conditions,
Hence

V_{1} = 22.4

litre,

V_{2} = ?

For isothermal and reversible expansion,

Δ E = 0

∴ q = - W

= - [- n RT \times 2.303 lo g V_{2} / V_{1}]

or

100 \times 4.184 J

= 1 \times 8.314 \times 273 \times 2.303 \times lo g \frac{V _{2}}{22.4}

or

4184 = 5227.17 lo g \frac{V _{2}}{22.4}

or

\frac{V _{2}}{22.4} =

antilog

0.8004

V_{2} = 121.25 m l

Q. One mole of an ideal gas is initially at 0∘C and 1 atm pressure. If it absorbs 1000 cal heat during a reversible isothermal expansion, what will be its final volume?

102.5 litre

242.5 litre

22.4 litre

121.25 litre

Since the gas is under S.T.P conditions, Hence V1​=22.4 litre, V2​=? For isothermal and reversible expansion, ΔE=0 ∴q=−W =−[−nRT×2.303logV2​/V1​] or 100×4.184J =1×8.314×273×2.303×log22.4V2​​ or 4184=5227.17log22.4V2​​ or 22.4V2​​= antilog 0.8004 V2​=121.25ml

Q. One mole of an ideal gas is initially at $0^{\circ} C$ and $1$ atm pressure. If it absorbs $1000$ cal heat during a reversible isothermal expansion, what will be its final volume?