Question

A certain amount of gas is enclosed in a sphere of volume 5L at pressure 7atm and temperature 327°C. It
is then connected to another sphere of volume 2.5 L by a narrow tube and stopcock. The second sphere is
initially evacuated and the stopcock is closed. After opening the stopcock, the temperature of gas in the
second sphere becomes 127°C, while the first sphere is maintained at 327°C. Find the final gas pressure
within the two spheres.​

Answer 1

Explanation:

The final pressure in the two spheres can be found by using the ideal gas law and the idea that the internal energy of an ideal gas is a function of temperature only, and not of pressure or volume.

The ideal gas law states that PV = nRT, where P is pressure, V is volume, n is the number of moles, R is the ideal gas constant, and T is temperature.

We know that the initial pressure in the first sphere is 7atm, and the initial temperature is 327°C. By using the ideal gas law, we can find the number of moles of gas in the first sphere:

n1 = (7atm * 5L) / (8.314 J/mol.K * (327+273.15))

We know that the temperature in the second sphere is 127°C after the stopcock is opened, and the volume is 2.5L. We can use the ideal gas law to find the final pressure in the second sphere:

P2 = (n1 * R * (127+273.15)) / (2.5L)

Now that we know the pressure and temperature of the two spheres, we can use the fact that the internal energy of an ideal gas is a function of temperature only to find the final pressure within the two spheres.

U = nCvT

So the internal energy of the first sphere is equal to the internal energy of the second sphere:

n1Cv(327+273.15) = n2Cv(127+273.15)

Therefore, we can conclude that:

n1(327+273.15) = n2(127+273.15)

And since n1 is known, we can find n2:

n2 = n1(327+273.15) / (127+273.15)

Finally, we can use the ideal gas law to find the final pressure in the first sphere:

P1 = (n2 * R * (327+273.15)) / (5L)

The final pressure within the two spheres is P1