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A moles of a monoatomic ideal gas are at...

A moles of a monoatomic ideal gas are at pressure `3xx10^(5)Nm^(-2)` and temperature 100K (state A, say). Is is head heated isobarically to temperature 400K (state B, say). Next it undergoes isothermal expansion to pressure `1 xx 10^(5) Nm^(-2)` (state C). It is then cooled isobarically to 100 K (state D). Finally, it is compressed isothermal to returm to its initial state A. Draw P-T : P-V and V-T diagrams for the whole process.

Text Solution

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Here `mu = 4`
At state `A, P= 3 xx 10^(5)Nm^(-2), T = 100 K`
Using `PV = mu RT`
`V = (mu RT)/(P) = (4 xx 8.3 xx 100)/(3 xx 10^(5)) = 11.07 xx 10^(-3)m^(3)`
This is the volume of gas at A.
In going from state B to state C,
Process is isothermal i.e., `T = consta nt = 400K`
At `C, P = 1 xx 10^(5)Nm^(-2)`
`:.` Volume of gas at state C,
`V = (mu RT)/(P) = (4 xx 8.3 xx400)/(1 xx 10^(5)) = 132.8 xx 10^(-3)m^(3)`
In going from state C to D the pressure is isobaric
`:. P = 1 xx 10^(5) Nm^(-2) , T = 100K`
`:.` Volume of gas at state D,
`V = (mu RT)/(P) = (4 xx 8.3 xx 100)/(1 xx 10^(5)) = 33.2 xx 10^(-3)m^(3)`
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