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. a) W=-198.7cal b) P= 0.694atm
• B. a) W=+198.7cal b) P= 0.694atm
• C. a) W=-198.7cal b) P= 0.794atm
• D. None of these

Answer 1

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

$w=-P\cdot \Delta V=-P(V_2-V_1)$

$=-P\left[{(nRT}_2/P\right)-\left({nRT}_1/P)\right]$

$=-nR(T_2-T_1)=-1\times 1.987\times (373-273)$

$=-198.7cal$

(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 $P_1$

$W_R=-2.303nRT\log \left(P/P_1\right)$

$-198.7=-2.303\times 1.987\times 273\log \left(1/P_1\right)$

$\therefore P_1=0.694atm$