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Standard XII

Physics

Pressure

A balloon has...

Question

A balloon has a volume of $0.09 m^{3}$ below the surface of the water (density $= 10^{3} {kg/m}^{3}$ ) at a depth of $40 m$ . If the temperature remains constant, what is its volume in $m^{3}$ when it is at the surface where the pressure is $1 \times 10^{5} {N/m}^{2}$

0.43

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0.45

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0.36

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0.51

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Solution

The correct option is B $0.45$
Gas inside the balloon obeys isothermal process
So, $[P V = n R T]$
$P_{1} V_{1} = P_{2} V_{2}$
$[P_{0} + ρ g h] [0.09] = P_{0} V_{2}$
$[1 \times 10^{5} + 10^{3} \times 10 \times 40] [0.09] = 1 \times 10^{5} \times V_{2}$
$5 \times 10^{5} \times 0.09 = [1 \times 10^{5}] V_{2}$
$V_{2} = 0.45 m^{3}$
Hence option (B) is correct.

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A balloon has a volume of 0.09 m3 below the surface of the water (density =103 kg/m3) at a depth of 40 m. If the temperature remains constant, what is its volume in m3 when it is at the surface where the pressure is 1×105 N/m2

The correct option is B 0.45Gas inside the balloon obeys isothermal process So, [PV=nRT] P1V1=P2V2 [P0+ρgh][0.09]=P0V2 [1×105+103×10×40][0.09]=1×105×V2 5×105×0.09=[1×105]V2 V2=0.45 m3 Hence option (B) is correct.

A balloon has a volume of $0.09 m^{3}$ below the surface of the water (density $= 10^{3} {kg/m}^{3}$ ) at a depth of $40 m$ . If the temperature remains constant, what is its volume in $m^{3}$ when it is at the surface where the pressure is $1 \times 10^{5} {N/m}^{2}$