0.75 kg of air is compressed in a piston cylinder from 100°C and 50kPa to 25°C.
ID: 477400 • Letter: 0
Question
0.75 kg of air is compressed in a piston cylinder from 100°C and 50kPa to 25°C. If the piston cylinder is fitted with a set of stops such that the air can be compressed to a minimum volume of 1.4m3, is it possible for the process to take place at constant pressure? IF YOU CHOOSE TO MODEL AIR AS AN IDEAL GAS, YOU MUST SHOW WHY THIS IS A VALID ASSUMPTION!!!!
The compressibility factor Z = .87 (if i calculated it right) and our professor said if Z>= .9 then it can be considered an ideal gas. So this isn't an ideal gas?
Explanation / Answer
Given that;
Mass of air = 0.75 kg
T1= 100°C or 373 K and P1 = 50kPa = 50*10^Pa
T2=25°C or 298 K and V2 = 1.4 m^3
First calculate the value of V1 from ideal gas law as follows:
PV = m RT
V = m RT /P
R = Gas constant 287.05, gas constant for dry air, J/(kg*degK)
V= 0.75 * 287.058 *373 /50*10^3
= 1.61 m^3
At constant pressure:
V1/T1 = V2 /T2
1.61 m^3/373= 1.4 /298
4.32*10^-3 = 4.69*10^-3
Here both side are approximately equal thus this process from 1-à 2 can be possible at constant pressure.
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