Question

The gas at 300K is at pressure of 80cm of mercury. Find the final pressure of the gas if it is heated to 400K at constant volume.

Answer 1

Since the volume of gas in thermometer is constant,

T

1

P

1

=

T

2

P

2

Since temperature of melting ice is 273.15K,

273.15

80

=

T

2

160

T

2

=2(273.15)K=546.30K

Answer is 546.30K

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Answer 2

The final pressure of the gas is heated to 400K at a constant volume is 106.7 cm of mercury.

Given:

The gas at 300K is at a pressure of 80cm of mercury.

To Find:

The final pressure of the gas is heated to 400K at a constant volume.

Solution:

To find the final pressure we will follow the following steps:

As we know,

For an ideal gas,

The relation between temperature pressure and volume for 1 mole is given by:

$pv = rt$

Here,

p is pressure, v is volume and t is temperature.

Now,

At constant volume, pressure is directly proportional to temperature.

So,

$\frac{p1}{p2} = \frac{t1}{t2}$

Now,

According to the question,

p1 = 400 K

p2 =80 cm of mercury

t1 =?

t2 = 300 K

Now,

In putting values we get,

$\frac{p1}{80} = \frac{400}{300}$

$p1 = \frac{4 \times 80}{3} = \frac{320}{3} = 106.7 \: cm \: of \: mercury$

Henceforth, The final pressure of the gas is heated to 400K at a constant volume is 106.7 cm of mercury.

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