Question

1-1) Arrange three cups filled with water. Put cold water in the first cup together with an ice cube, put hot water (not too hot for your hand) in the second cup and have the third cup at body temperature. Now, put one hand in the cold water and the other hand in the hot water for half a minute or so then put them both in the lukewarm cup. What did you experience? Decide if you think that your skin is a good thermometer, or is only sensitive to changes in temperature.

1-2) Two containers of ideal gases are in thermal equilibrium with each other. Which of the following must be the same for the two gases? Explain your answer for each property below. (a) Temperature (b) Pressure (c) Average kinetic energy per molecule (d) Average speed of the molecules.

Answer 1

1-1) First of all our senses are relative. When you put your hand in the cup filled with cold water after some time your hand tries to attain a thermal equillibrium with the cold water and as a result the temperature of your hand drops. Opposite case occurs when you put your hand in the cup containing warm water. Now whenever we judge either temperature or how bright a light source is, we dont judge the absolute temperature or the absolute brightness of light. In fact we try to judge them relative to other things around them. So when you put both of your hands together in the cup containing water with temperature comparable to your body your senses get confused. As the temperature sensors in your hand judge the temperature of the water relative to your hand. So for the hand which was kept in the cold water the third cup now feels warm whereas for the other hand whichw as in the hot water bath now feels cold.

Measuring the temperature with respect to one object (your hand in this case) is fine if that reference point stays at a constant value. However in this case when you put your hand inside the cold water cup (or the hot one) for a long time the temperature of your hand starts to drop and as a result your reference point for judging has also shifted. So water which once felt at the same temperature as your body now feels warm. So we can conclude that our skin is sensitive to temperature and it cannot be considered as a good thermometer.

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1-2) a) The gases will attain thermal equilibrium when the temperature of the two containers become same. Energy exchange takes place in this case.

b) Two systems can be in thermal equilibrium at different pressure.

c) Average kinetic energy per molecule of an ideal gas is given by , where is the Boltzmann constant. So at thermal equilibrium average kinetic energy will also be same as the temperature remains the same.

d) The average speed of the molecules is given by , where R is the universal gas constant and M is the molecular mass. Now if the gases are same then the average speed will also be same. However for different gases at thermal equilibrium the average speed will be different.