Answer to Question #102155 in Mechanical Engineering for Usman

Question

A container (with a movable piston) contains 20.0 L of compressed nitrogen gas at 10.0 bar and 25.0 oC. Calculate q, w, ∆ U and ∆H as one lets the gas expand reversibly and isothermally to a pressure of 1.00 bar.

Answer 1

For isothermally process

$T=const$

or

$p_1V_1=p_2V_2=const$

$\Delta U=\nu C_V \Delta T=0$

$W=\frac{m}{M}RT \ln \frac{p_1}{p_2}$

$p_1V_1=\frac{m}{M}RT$

So,

$W=\frac{m}{M}RT \ln \frac{p_1}{p_2}=p_1V_1\ln \frac{p_1}{p_2}=1000000 \cdot0.02\cdot\ln \frac{1000000}{100000}\approx46 kJ$

$q=\Delta U+W=0+46=46 kJ$

$H=U+pV$

$H_1=U_1+p_1V_1$

$H_2=U_2+p_2V_2$

$\Delta H=\Delta U+p_2V_2-p_1V_1=0+p_2V_2-p_1V_1=p_2V_2-p_1V_1=0$

Answer. $W=46 kJ,q=46kJ,\Delta U=0,\Delta H=0.$