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Standard XII

Physics

Conduction Law

A piston-cyli...

Question

A piston-cylinder device initially contains $0.07 m^{3}$ of nitrogen gas at $130 k P a$ and $120^{o} C$ . The nitrogen is now expanded polytropically to a state of $100 k P a$ and $100^{o} C$ . Determine the Boundary work of the process.

1.86 k J

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1.68 k J

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6.81 k J

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8.18 k J

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Solution

The correct option is B $1.86 k J$
Initial pressure= $P_{i} = 130 k P a$ , initial temperature= $T_{i} = 393 K$ , initial volume= $V_{i} = .07 m^{3}$
Final pressure= $P_{f} = 100 k P a$ , final temperature= $T_{f} = 373 K$ , final volume= $V_{f}$

For polytropic process, $P V^{x}$ =constant
Here $P_{i} V_{i}^{x} = P_{f} V_{f}^{x}$ ..........(i)
Applying ideal gas equation, $V_{f} = \frac{(P_{i} V_{i} T_{f})}{(T_{i} P_{f})} = \frac{130 \times .07 \times 373}{393 \times 100}$
$\Rightarrow V_{f} = 0.086 m^{3}$
Hence putting these values in (i),
x=1, i.e. PV=constant $\to$ process is isothermal.
Hence work done = $P_{i} V_{i} ln \frac{V_{f}}{V_{i}} = 1.86 k J$

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A piston-cylinder device initially contains 0.07m3 of nitrogen gas at 130 kPa and 120oC. The nitrogen is now expanded polytropically to a state of 100 kPa and 100oC. Determine the Boundary work of the process.

A piston-cylinder device initially contains $0.07 m^{3}$ of nitrogen gas at $130 k P a$ and $120^{o} C$ . The nitrogen is now expanded polytropically to a state of $100 k P a$ and $100^{o} C$ . Determine the Boundary work of the process.