MCQ: Ideal Gas Flow Out of Balloon with Temp Increase

[kalupahana]

Homework Statement

A balloon with a constant volume is in 100⁰C. The fraction of gas flow out of balloon when temperature increased by 2⁰C is nearly equal to
(consider pressure and the gas in balloon is ideal)

a. 2/373
b. 2/375
c. 2/100
d. 373/375
e. 100/102

Homework Equations

PV=nRT
P-pressure
V-volume
n-number of mols
R-universal gas constant
T-temperature

The Attempt at a Solution

In these conditions P,n & R is constant
∴ V α T
V₁/V₂=T₁/T₂
V₁/V₂=375/373

the amount flow out = 375/373-1 = 2/373

but the answer given as as 2/375
the book i get this considered the mass is increasing when temperature increases

in book that was like

PV=(m/M)RT
P,V,M and constant (m-mass of gas, M-molar mass)

m α 1/T
m₁T₁=m₂T₂
m₁/m₂=373/375

the mass flow out = 1-373/375=2/375

which is right

 

[ehild]

A balloon with a constant volume is in 100⁰C. The fraction of gas flow out of balloon when temperature increased by 2⁰C is nearly equal to
(consider pressure and the gas in balloon is ideal)

The Attempt at a Solution

In these conditions P,n & R is constant
∴ V α T
V₁/V₂=T₁/T₂
V₁/V₂=375/373...

the amount flow out = 375/373-1 = 2/373

but the answer given as as 2/375

The volume of the balloon is constant, but n, the amount of gas in it is different. The pressure is the same at both temperature. You have the equations

PV=n₁ R T₁
and
PV=n₂ R T₂.

ehild