Work done on 3 moles of an ideal gas at 27° C, if it is compressed reversibly and isothermally from a pressure of 1.01 × 105 N m -2 to 5.05 × 106 N m -2 is kJ. [Given log 10(2)=0.3010]

Question

Work done on 3 moles of an ideal gas at 27° C, if it is compressed reversibly and isothermally from a pressure of 1.01 × 105 N m -2 to 5.05 × 106 N m -2 is kJ. [Given log 10(2)=0.3010] (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

For reversible process under isothermal conditions,

w = - 2.303 n RT lo g_{10} \frac{P _{1}}{P _{2}}

= - 2.303 \times 3 \times 8.314 \times 300 lo g_{10} \frac{1.01 \times 1 0 ^{5}}{5.05 \times 1 0 ^{6}}

= - 2.303 \times 3 \times 8.314 \times 300 \times lo g_{10} (2 \times 1 0^{- 2})

= 2.9277 \times 1 0^{4} J = 29.28 k J

Q. Work done on 3 moles of an ideal gas at 27∘C, if it is compressed reversibly and isothermally from a pressure of 1.01×105Nm−2 to 5.05×106Nm−2 is______ kJ. [Given log10​(2)=0.3010]

For reversible process under isothermal conditions, w=−2.303nRTlog10​P2​P1​​ =−2.303×3×8.314×300log10​5.05×1061.01×105​ =−2.303×3×8.314×300×log10​(2×10−2) =2.9277×104J=29.28kJ

Q. Work done on $3$ moles of an ideal gas at $2 7^{\circ} C$ , if it is compressed reversibly and isothermally from a pressure of $1.01 \times 1 0^{5} N m^{- 2}$ to $5.05 \times 1 0^{6} N m^{- 2}$ is______ $k J$ .
[Given $lo g_{10} (2) = 0.3010$ ]