Question

The volume V of gas varies inversely to the pressure P. The volume of a gas is200 cm3
under
pressure of 32 kg/cm2
. What will be its volume under pressure of 40 kg/cm2
?

Answer 1

The volume V of gas varies inversely to the pressure P. The volume of a gas is 200 cm^3 under pressure of 32 kg/cm^2. What will be its volume under pressure of 40 kg/cm2?
-------------
P*V = k
200*32 = V*40

Answer 2

Gas volume under pressure of 40 $kg/cm^{2}$will be $160 cm^{3}$.

Step-by-step explanation:

Given:

The volume V of gas varies inversely to the pressure P.

The volume of  gas is 200 cm3 under pressure of 32 kg/cm2.

The gas under pressure is  40 kg cm2.

To Find:

Gas volume under pressure of 40 kg cm2.

Formula Used:

As per Boyle's law  for a fixed mass of gas at constant temperature, the absolute pressure and the volume of a gas are inversely proportional.

$P_{1} \times V_{1} =P_{2} \times V_{2}$   ---------- formula no.01.

Where,

$P_{1}\ and\ P_{2}$  are pressure of gas

$V_{1}\ and\ V_{2}$  are volume of gas

Solution:

As given,the volume of a gas is 200$cm^{3}$ under pressure of 32$kg/cm^{2}$.

$P_{1} = 32 kg/cm^{2} \ and \ V_{1}=200 \ cm^{3}$

As given, the gas under pressure is  40 $kg/cm^{2}$

$P_{2} = 40kg/cm^{2} \ and \ V_{2}= ?$

Applying formula no.01.

$P_{1} \times V_{1} =P_{2} \times V_{2}$

$32 \times 200 =40 \times V_{2}$

$V_{2}=\frac{6400}{40}$

$V_{2}= 160 cm^{3}$

Thus,gas volume under pressure of 40 $kg/cm^{2}$will be $160 cm^{3}$.

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