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Relation between P, V, T, Gamma in Adiabatic Proceses

One mole of a...

Question

One mole of an ideal gas is heated at constant pressure from $0^{o}$ C to $100^{o}$ C. (a) Calculate work done. (b) If the gas is expanded isothermally and reversibly at $0^{o}$ C from 1 atm to some other pressure $P_{1}$ . what must be the final pessure if the maximum work is equal to the work involved in (a)?

a) W=-198.7cal b) P= 0.694atm

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a) W=+198.7cal b) P= 0.694atm

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a) W=-198.7cal b) P= 0.794atm

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None of these

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Solution

The correct option is A a) W=-198.7cal b) P= 0.694atm
(a) Work done during heating of gas from $0^{o}$ C to $100^{o}$ C under isobaric process is
$w = - P \cdot Δ V = - P (V_{2} - V_{1})$

$= - P [{(n R T}_{2} / P) - ({n R T}_{1} / P)]$

$= - n R (T_{2} - T_{1}) = - 1 \times 1.987 \times (373 - 273)$

$= - 198.7 c a l$
(b) If work equivalent to 198.7 cal is used for gas at $0^{o}$ C, causing it isothermal compression, from 1 atm to pressure $P_{1}$
$W_{R} = - 2.303 n R T log (P / P_{1})$
$- 198.7 = - 2.303 \times 1.987 \times 273 log (1 / P_{1})$

$∴ P_{1} = 0.694 a t m$

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One mole of an ideal gas is heated at constant pressure from 0oC to 100oC. (a) Calculate work done. (b) If the gas is expanded isothermally and reversibly at 0oC from 1 atm to some other pressure P1. what must be the final pessure if the maximum work is equal to the work involved in (a)?