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Q.

It is known that for a given mass of gas, the volume (V) varies inversely as the pressure (P). If at a time volume of gas for a fixed mass is $60 c m^{3}$ at pressure 1.5 atmosphere, then find the pressure at volume $100 c m^{3}$ .

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a

0.9

b

0.8

c

1.0

d

1.1

answer is A.

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Detailed Solution

Given that for a given mass of gas, the volume (V) varies inversely as the pressure (P).
We need to find that if at a time, the volume of gas for a fixed mass is

60 c m^{3}

at pressure 1.5 atmosphere.
Assume that the pressure at volume 100 cm³ is P atmosphere.
Using the given information that for a given mass of gas, the volume (V) varies inversely to the pressure (P).

V \times P = k

Equate the product of 1.5 atmosphere and 60 cm³ with product of P atmosphere with 100 cm³ and solve for P.

P \times 100 = 1.5 \times 60

\Rightarrow P = \frac{90}{100}

\Rightarrow P = 0.9

The pressure at volume 100 cm³ is 0.9 atmosphere.
Hence, the correct option is 1.

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