Question

If the volume of a given mass of a gas is doubled without changing its temperature, the pressure of the gas is reduced to:

*1/2 of the initial value
*1/3 of the initial value
*1/4 of the initial value
*2/3 of the initial value ​

Answer 1

Explanation:

Two balls of charges q1 and q2, initially have exactly same velocity. Both the balls are subjected to same uniform electric field for same time. As a result , the velocity of the first ball is reduced to half of its initial value and its direction changes by 60° .The direction of the velocity of second ball is found to change by 90.

The electric field and initial velocity of the charged particle are inclined at angle

1)60. (2)30

3) 90. (4)150

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Answer 2

The value of the pressure of the gas is reduced to 1/2 of the initial value and option (1) is correct.

Explanation:

Given:

If the volume of a given mass of a gas is doubled without changing its temperature.

To Find:

The value of the pressure of the gas is reduced to.

Formula Used:

As per Boyle's law,for a gas, the relationship between volume and pressure (at constant mass and temperature) can be expressed  as below-

$P\propto \frac{1}{V}$

$P=k V$

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

Where

$P_{1}$ = the initial pressure exerted by the gas

$V_{1}$ = the initial volume  the gas

$P_{2}$  = the final pressure exerted by the gas

$V_{2}$ = the final volume  the gas

Solution:

Let  the initial volume of a given  mass of a gas is v.

Let  the initial pressure  of a given  mass of a gas is p.

As given-If the volume of a given mass of a gas is doubled without changing its temperature.

$V_{1}= v$        and   $V_{2}=2v$

$P_{1}=p$       and  Temperature is constant.

Applying the formula no.01

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

$p \times v =P_{2}\times 2v$

$P_{2}=\frac{p \times v}{2v}$

$P_{2}=\frac{p }{2}$

The value of the pressure of the gas is reduced to 1/2 of the initial value.

Thus,the value of the pressure of the gas is reduced to 1/2 of the initial value and option (1) is correct.

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