Question

1)Two rigid tanks of equal size and shape are filled with different gases. The tank on the left contains oxygen, and the tank on the right contains hydrogen. Assume both gases are ideal. The molar masses of oxygen and hydrogen are 32 and 2, respectively. Both containers are at the same temperature. A pressure gauge is pin oxygen hydrogen connected to each tank. Both gauges show a reading of 230 kPa.

Is the number of oxygen molecules in the left container greater than, less than, or equal to the number of hydrogen molecules in the right container? Explain your reasoning.

2)

A cylindrical pump contains one mole of an ideal gas. The piston is free to move, but no gas can enter or leave the pump. Neglect friction between the piston and the cylinder walls.

The piston is quickly pressed inward as shown in the diagram. A sensor in the pump records an increase in temperature.

a. How can you account for the increase in temperature of the gas? Explain.

b. Did the thermal energy of the gas increase, decrease, or remain the same in this process? Explain.

Answer 1

1.First of all, you have to know what temperature actually means. Its actually a measure of the average linear kinetic energy of all the gas particles. If two gases have the same kinetic energy, that means that the average linear kinetic energy of both the gases are equal. That is, the average value of ¹/₂mv² of both the gases is equal.

If you apply this, we can actualy get the ideal gas equation.

ie. PV=nRT

Since pressure, volume, temperature are the same in both gases, and R is a constant, n in both cases has to be equal. Which actually states that the number of moles of the gas particles in both the containers are equal.

This is also the avagadro's law, you can look it up.

2.I'm gonna answer the second part first. The thermal energy depends only on the temperature. As i have explained below temperature is directly proportional to the average linear kinetic energy. Thermal energy is the same as the total linear kinetic energy. Thus, for the same number of particles, the gas's thermal energy is directly proportional to the temperature of the gas. And so, since in this case, the temperature increased without a change in the number of particles, the thermal energy is increased.

Now the first part of the question can be also put as, how does the thermal enery increase on compression of the pistonthereby increasing the temperature. Imagine an elastic ball hitting a wall. It will bounce back with the same speed it hit. But imagine what happens when the wall is moving towards the direction of the ball. The ball rebounds with a greater speed. Didn't the ball gain energy? Where from does this xtra energy come? It comes from the force which is required to push the wall. Same way, the moving piston increases the energy of the gas and the enegy is provided by the force pushing the piston.

hope that answers ur question