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Work Done in Isothermal Reversible Process

A piston-cyli...

Question

A piston-cylinder device initially contains $0.4 m^{3}$ of air (to be treated as an ideal gas) at 100 kPa and $80^{o} C$ . The air is now isothermally compressed to $0.1 m^{3}$ . The work done during this process is kJ.
(Take the sign convention such that work done on the system is negative)
-55.45

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Solution

The correct option is A -55.45
$V_{1} = 0.4 m^{3};$ $p_{1} = 100 k P a$
$T_{1} = 80^{o} C = (80 + 273) K = 353 K$
$V_{2} = 0.1 m^{3}$
For isothermal process

$W = p_{1} V_{1} l o g_{e} \frac{V_{2}}{V_{1}}$
$= 100 \times 0.4 l o g_{e} \frac{0.1}{0.4}$
$= - 55.45 k J$

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