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Grade: 12th pass
        
The maximum capacity of bollowns A and B are 800ml and 1800ml which are bollown A and B brust first if temperature is gradually increase
2 months ago

Answers : (2)

Lavesh Gupta
38 Points
							
We can easily apply, V1/T1 = V2/T2 to get the answer since the pressure, number of moles are constant for gas in each of the baloon. We’ll need inital volume for both the baloons as well as their temperatures.
2 months ago
AKSHANSH PAREEK
68 Points
							

The balloon with larger capacity (1800 ml) will burst first.

(Here, it is assumed, balloon wall materials and gas inside spherical balloon (air) are same for both cases. And, balloon wall is thin (r/T>10), so thin walled spherical pressure vessel formula can be applied.)

Equations for determining tangential tensile stress (hoop) developed at thin balloon wall:

σ=Pr/2t.........(1)

(radial stress at inner wall ‘–P’ will be very less compared to hoop stress, so neglected.)

Gas law Equations in terms of density and specific R_specific (R_specific= R/M):

P=ρX R_specificXT.........(2)

(density, ρ and specific gas constant, R_specific is intrinsic properties of a gas, so it will be same for the same gases present in both balloons.)

From equation (1) & (2) and by partial differentiation,

dσ = (ρ X R_specific / 2t) X r X dT......(3)

so, rate of balloon wall’s stress increase is proportional to r (radius of spherical balloon).

So, balloon with larger capacity (greater volume means larger radius) will experience greater stress increase with increasing temperature. And ultimate stress at larger blloon will be crossed earlier than smaller balloon. So, larger balloon will burst first.

Here,

σ= Stress at balloon wall

P =Pressure inside balloon

r=Radius of spherical balloon

t= Thickness of balloon wall

ρ=Density of gas inside balloon

T= Temperature of gas inside balloon

R=Ideal or universal gas constant

M=Molar mass of gas inside balloon

R_specific=R/M=Specific gas constant of gas inside balloon

 

please approve

 

2 months ago
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