Question

Nitrogen is contained in a 80-L tank and the initial pressure and temperature is 250 kPa and 200 ⁰C, respectively.

Determine:

a. the mass of the gas in kg.

b. Now, if 0.05 kg of gas leaks out of the tank and in the process the temperature drops to 33 ^oC. Find the gage pressure of the gas remaining in the tank in kPa, if the atmospheric is 100 kPa.

a. m = _____ kg Answer in 3 decimal places

b. P = _____ kPag

Answer 1

Solution;

Given;

Volume of tank,V=80-L=0.08m³

Initial pressure,p=250kPa

Temperature,T=200°C=473K

Gas constant,R=296.8J/kgK

(a)mass of gas in kg;

Using ideal gas equation;

pV=mRT

$m=\frac{pV}{RT}$ =$\frac{250×10^3×0.08}{296.8×473}$ =$0.1425$

Mass of the gas;

$m=0.142kg$

(b)

Remaining mass;

$m'=0.1425-0.05$ =0.0925kg

Pressure,$p=100kPa$

T'=33°C=306K

From the ideal gas equation;

$p=\frac{mRT}{V}$ =$\frac{0.0925×296.8×306}{0.08}$

$p=105011.55$ Pa

$p=105.011kPa$

Answers;

a.m=0.142kg

b.P=105.011kPa