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Ideal Gas Equation

An ideal gas ...

Question

An ideal gas undergoes a reversible process in which the pressure varies linearly with volume. The conditions at the start (subscript 1) and at the end (subscript 2) of the process with usual notation are : $p_{1} = 100 k P a, V_{1} = 0.2 m^{3}$ and $p_{2} = 200 k P a, V_{2} = 0.1 m^{3}$ and the gas constant, required for the process (in kJ) is
15

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Solution

The correct option is A 15
Given: $p_{1} = 100 k P a, V_{1} = 0.2 m^{3}$
$p_{2} = 200 k P a, V_{2} = 0.1 m^{3}, R = 0.275 k J / k g K$
$p \propto V$
$∴$ p-V diagram will be a straight line

$∴$ Work $= \frac{1}{2} (100 + 200) \times (0.2 - 0.1)$
$= 15 k J$
The work is done on the gas, since the process is compression.
Since only magnitude is asked hence final answer is without ve sign.
POINTS TO REMEMBER
Whenever it is given in the problem that pressure varies linearly with volume,
Always use,
Work done, $W = \frac{1}{2} (p_{1} + p_{2} (V_{2} - V_{1})$

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P_{1} = 100 kPa, V_{1} = 0.2 m^{3}

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