Question

A reservoir contains 2.83 cubic meter of CO at 6895 kPa and 23.6 degrees C. A cylindrical tank with h=1.5D is filled from the reservoir to a pressure of 3697 kPa and a pressure of 3697 kPa and a temperature of 15.4 degrees C, while the pressure and temperature in the reservoir decreases to 6205 kPa and 18.3 degrees C respectively.a) the total mass of CO transferred to the tank in kg, b) the total volume of the tank in cubic meter, c) the diameter of the tank in mm

Answer 1

Solution;

Given;

$V_{co}=2.83m^3$

$P_{r1}=6895kPa$

$P_{r2}=6205kPa$

$P_t=3697kPa$

$T_{r2}=18.3°c=291.3K$

$T_t=15.4°c=288.4K$

$T_{r 1}=23.6°c=296.6K$

(a)

Calculate mass in reservoir before transferring;

$m_{r1}=\frac{P_{r1}V_{co}}{RT_{r1}}=$ $\frac{6895×2.83}{0.2968×296.6}=221.64kg$

Mass in reservoir at end of transfer;

$m_{r2}=\frac{6205×2.83}{0.2968×291.3}=203.09kg$

Mass of CO transfer to the tank is;

$m_t=m_{r1}-m_{r2}=221.64-203.09=18.56kg$

(b)

Volume of the tank;

$P_tV_t=m_tRT_t$

$V_t=\frac{m_tRT_t}{P_t}=\frac{18.56×0.2968×288.4}{3697}$

$V_t=0.43m^3$

(c)

Diameter of the tank;

$V=πr^2h$

$0.43=\frac{π}{4}×D^2×1.5D$

$D^3=0.365m^3$

$D=0.7147m$

$D=714.7mm$