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Poisson's Effect

In a process,...

Question

In a process, the pressure and volume of a given mass of gas increase. Then :

A

it is impossible

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B

the system does a positive work

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C

the temperature of the system must increase

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D

Δ Q = Δ U

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Solution

The correct options are
B the temperature of the system must increase
C the system does a positive work
Given that pressure and volume increase
$P_{2} > P_{1}$ and $V_{2} > V_{1}$
From ideal gas law
$\frac{P_{1} V_{1}}{T_{1}} = \frac{P_{2} V_{2}}{T_{2}}$
$\frac{P_{1} V_{1}}{T_{1}} = \frac{P_{2} V_{2}}{T_{2}} T_{2} = \frac{P_{2} V_{2}}{P_{1} V_{1}} T_{1} (\frac{P_{2}}{P_{1}} > 1, \frac{V_{2}}{V_{1}} > 1)$
Then temperature of the system will also increase
$W o r k = \int_{1}^{2} P d V$
Since $V_{2} > V_{1}$
The system will do a positive work.

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