Consider a well-insulated horizontal rigid cylinder that is...

Consider a well-insulated horizontal rigid cylinder that is divided into two compartments by a piston that is free to move but does not allow either gas to leak into the other side. Initially, one side of the piston contains $1 \mathrm{m}^{3}$ of $\mathrm{N}_{2}$ gas at $500 \mathrm{kPa}$ and $120^{\circ} \mathrm{C}$ while the other side contains $1 \mathrm{m}^{3}$ of He gas at $500 \mathrm{kPa}$ and $40^{\circ} \mathrm{C}$. Now thermal equilibrium is established in the cylinder as a result of heat transfer through the piston. Using constant specific heats at room temperature, determine the final equilibrium temperature in the cylinder. What would your answer be if the piston were not free to move?

Transcript

00:02 Hi, in this question, the pressure of nitrogen on one compartment of the container, p1, n is given as 500 kilo -pascal.

00:18 The pressure of helium on the other compartment of the container, that is, p1 helium, is given as 500 kilopascal.

00:30 Similarly, the volume of the compartment 1 and compartment 2 both are 1 cubic meter, that is v1 of nitrogen is equal to v1 of helium is equal to 1 cubic meter.

00:51 We need to find the euclibrium temperature, te, in the cylinder.

00:58 First of all, let us find the mass of the nitrogen and helium.

01:06 To find the mass of the hydrogen and helium, we use the ideal gas equation, that is, b1n, b1n is equal to the mass of nitrogen multiply with r of nitrogen, multiply with the initial temperature of nitrogen.

01:28 The initial temperature of nitrogen is given as 120 degrees celsius, which is equal to 393 kelvin.

01:46 Now let us plug the given values and determine the mass of nitrogen.

01:53 This one is 500 kioskal, multiply with 1 cubic meter, is equal to mass of nitrogen.

02:00 Nitrogen multiply with 0 .297 kilojoules per kg kelvin multiply with 393.

02:11 On calculation we obtained the mass of nitrogen mn is equal to 4 .28 kg.

02:25 Now let us determine the mass of helium using the same relation.

02:30 That is p1 h v1 h is equal to m h r h into t1 h the initial temperature of helium is given as 40 degrees celsius 40 degrees celsius 40 degrees celsius is equal to 313 kelvin now let us plug the given values and determine the mass of helium.

03:06 This is 500 multiply with 1 is equal to mass of helium multiply with 2 .08 kilojoules per kg kelvin multiply with 313.

03:25 On calculation we obtained the mass of helium mh is equal to 0 .768 kg.

03:40 Now let us find the equilibrium temperature using the energy balance equation...

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