Answer to Question #204109 in Mechanical Engineering for samuel

Question

an insulated cylinder device contains 2kg of water as expands at a constant pressure of 175 kpa. the initial volume and specific enthalpy of the water are 0.5m^3 and 485kJ/kg, respectively. the water is stirred by a paddle wheel amounting work transfer of 400 kJ while a current of 8A flows for 45min through a resistor placed in the water. if the final specific volume and specific enthalpy are 1.25m^3/kg and 1594 kJ/kg,respectively; determine 1.the boundary work done

2.the voltage of the source

Answer 1

1.The boundary work done

The boundary work is done during the polytropic process

$W= \frac{P_1V_1-P_2V_2}{n-1}$ But we know that $PV^n=C \implies P_1V_1^n=P_2V_2^n \implies \frac{P_1}{P_2}=(\frac{V_2}{V_1})^n$

$\frac{175}{P_2}=\left(\frac{1.25}{0.5}\right)^{1.67}$

$P_2=\frac{175\cdot \:0.5^{1.67}}{1.25^{1.67}}=37.88595 kPa$

$W= \frac{P_1V_1-P_2V_2}{n-1}= \frac{175*0.5-37.89*1.25}{1.67-1} = 59.91 kJ$

2.The voltage of the source

$P=IV \implies \frac{W}{t}=IV \implies V=\frac{W}{It}$

$V=\frac{400*10 ^3}{45*60*8}= 18.52 V$