Question

A balloon is filled upto 3/4th of its maximum stretching capacity at 27° celcius.To what temp the can be safely heated at constant pressure?

Answer 1

Answer:

ideal gas equation

PV=nRT

in the ques pressure is constant that means...

V/T=nRP=constant

V1/T1=V2/T2

T2=V2*T1/V1

Answer 2

Answer:

The temperature up to which balloon can be safely heated at constant pressure is $127^oC$.

Explanation:

Let maximum stretching of balloon is for volume = $V$

which is also equal to its final volume, $V_f=V$

Initially:

The volume of the balloon, $V_i=\frac{3}{4} V$

Temperature, $T_i = 27^oC=300K$

Final Volume, $V_f=V$

Final temperature = $T_f$

From the ideal gas equation,

$pV=nRT$

we can see that, at consatnt pressure $p$ : $V\propto T$

$\implies V=kT$     [where $k=\frac{nR}{V}=constant$]

Therefore, initially $V_i =k T_i$ ----(1)

finally, $V_f=kT_f$ ----(2)

Dividing equation (1)by (2), we get:

$\frac{V_i}{V_f} =\frac{kT_i}{kT_f}$

$\implies \frac{V_i}{V_f} =\frac{T_i}{T_f}$

$\implies \frac{\frac{3V}{4} }{V} =\frac{300}{T_f}$

$\implies T_f=\frac{4}{3} *300$

$\implies T_f=400K$

$\implies T_f=127^oC$

The temperature up to which balloon can be safely heated at constant pressure is $127^oC$.

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