Question

An airplane passenger has 100 cm3 of air in his stomach just before the plane takes off from a sea level airport. What volume (in cm3) will the air have at cruising altitude if cabin pressure is 7.50 ✕ 104 N/m2 , assuming that the temperature does not change?

Answer 1

Answer:

$134.7 cm^3$

Explanation:

We are given that

Initial volume=$V_i=100 cm^3$

Initial pressure=$P_i=P_a=1.01\times 10^5 Pa$

Final pressure=$P_f=7.5\times 10^4 N/m^2=7.5\times 10^4 Pa$

$1 N/m^2=1 Pa$

Temperature does not change

Therefore, Initial temperature=$(T_i)$=Final temperature($T_f)$

We know that

$PV=nRT$

$\frac{PV}{T}=nR=Constant$

$\frac{P_iV_i}{T_i}=\frac{P_fV_f}{T_f}$

Substitute the values

$\frac{1.01\times 10^5\times 100}{T_i}=\frac{7.5\times 10^4V_f}{T_i}$

$V_f=\frac{1.01\times 10^5\times 100}{7.5\times 10^4}$

$V_f=134.7 cm^3$

Hence, the air will have volume at cruising altitude=$134.7 cm^3$