Question

Example 3.4. A gas at a temperature of 20°C and a pressure of 1.5 bar occupies a volume of
0.1 m². If the gas is compressed to a pressure of 7.5 bar and a volume of 0.04 m, what will be the
final temperature of the gas.​

Answer 1

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Answer 2

Given:

The initial temperature of the gas = 20° C

The initial volume of the gas = 0.1 m²

The initial pressure of the gas = 1.5 bar

The final pressure of the gas = 7.5 bar

The final volume of the gas = 0.04 m²

To find:

The final temperature of the gas.

Solution:

We know from the ideal gas equation that

PV = nRT

It is given that

P1 = 1.5 bar = 150000 pascal; V1 = 0.1 m²; T1 = 20° C = 293 K; P2 =  7.5bar = 750000 pascal; V2 = 0.04 m²

Now

P1V1 = nRT1

nR = 150000 x 0.1 / 293 = 51.19

Now we will use this value to find the final temperature

P2V2 = nRT2

0.04 x 750000 = 51.19 x T2

T2 = 586.05 K = 313.05 ° C

therefore the final temperature of the gas will be 313.05 ° C.