5 moles of an ideal gas expand isothermally and reversibly from a pressure of 10 atm to 2 atm at 300k. What is the largest mass which can be lifted through a height of 1 meter in this expansion?

2041 kg

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2049 kg

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2409 kg

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4129 kg

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Solution

The correct option is B 2049 kg
The work done in an isothermal process can be given by:

$w = - n R T l o g_{e} \frac{P_{1}}{P_{2}}$

$w = - 2.303 \times 5 \times 8.314 \times 300 \times l o g (\frac{10}{2}) = - 20.075 \times 10^{3} J$

$M g h = M \times 9.8 \times 1$

$M \times 9.8 = 20.075 \times 10^{3}$

$M = 2048.469 k g$

$M ≅ 2049 k g$

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5 moles of an ideal gas expand isothermally and reversibly from a pressure of 10 atm to 2 atm at 300k. What is the largest mass which can be lifted through a height of 1 meter in this expansion?

The correct option is B 2049 kgThe work done in an isothermal process can be given by: w = −nRT logeP1P2 w = −2.303 × 5 × 8.314 × 300 × log(102) = −20.075 × 103 J Mgh = M × 9.8 × 1 M × 9.8 = 20.075 × 103 M = 2048.469 kg M ≅ 2049 kg