Question

one mole of an ideal gas expands from initial state (2V0, V0) to final state ( T0,2V0). The process of expansion is given by T =(- T0/V0 V+3T0) . Work done by the gas during the expansion is
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Answer 1

Explanation:

this problem is quite easy and interesting .you need a little knowledge of calculus. for answer refer to the image

Answer 2

The work done by the gas in during this expansion is  R$T_o$ [3ln - 2].

Given,

1 mole of an ideal gas

Initial volume = $V_o$

Final volume = 2$V_o$

Initial temperature = $T_o$

Final temperature = T

T = -$T_o$V/ $V_o$ + 3$T_o$

To find,

The work done by the gas in the expansion.

Solution,

We know the work done by the gas,

W = $\int\limits {P\,dV$

⇒ W = $\int {RT/V} \, dV$

⇒ W = -R$T_o$ + $\int{3RT_o} \, \frac{dV}{V}$

⇒ W = -R$T_o$ +  $3RT_o\int\limits^{2V}_{V_o}\frac {dV} {V}$

⇒ W = -R$T_o$ + 3R$T_o$  ×ln$2V_o$/$V_o$

⇒ W = 3R$T_o$ln2 - R$T_o$

⇒ W = R$T_o$ [3ln - 2]

So, we can conclude that the work, W, done by the gas in this expansion is  R$T_o$ [3ln - 2].

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