A closed gas cylinder is divided into two parts by a piston held

1.	A closed gas cylinder is divided into two parts by a piston held tight. The pressure and volume of gas in two parts respectively are( p, 5v) and (10p ,v). If now the piston is left free and the system undergoes isothermal process , then the volume of the gas in two parts respectively are.
Answer» Since the temperature is constant (isothermal process), we can apply Boyle’s law. The piston will move towards the lower pressure side until the pressures on the two sides are the same. If this common pressure is P’, we have P×5V + 10P×V = P’×6V, since the total volume is 6 V. From this, P’ = (15/6) P. Now, applying Boyle’s law to the gas on the two sides separarely, we have P×5V = (15/6) P×V₁ and 10P×V = (15/6) P×V₂ where V₁ and V₂ are the volumes of the gas in the two parts respectively. From the above equations, we obtain V₁ = 2V and V₂ = 4V.

A closed gas cylinder is divided into two parts by a piston held tight. The pressure and volume of gas in two parts respectively are( p, 5v) and (10p ,v). If now the piston is left free and the system undergoes isothermal process , then the volume of the gas in two parts respectively are.

Answer»

Since the temperature is constant (isothermal process), we can apply Boyle’s law.

The piston will move towards the lower pressure side until the pressures on the two sides are the same. If this common pressure is P’, we have

P×5V + 10P×V = P’×6V, since the total volume is 6 V.

From this, P’ = (15/6) P.

Now, applying Boyle’s law to the gas on the two sides separarely, we have

P×5V = (15/6) P×V₁ and

10P×V = (15/6) P×V₂

where V₁ and V₂ are the volumes of the gas in the two parts respectively.

From the above equations, we obtain V₁ = 2V and V₂ = 4V.

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