# Tag Info

115

I did the experiment. (dipping wins) H2O ice bath canning jar thermometer pot of boiling water stop watch There were four trials, each lasting 10 minutes. Boiling water was poured into the canning jar, and the spoon was taken from the ice bath and placed into the jar. A temperature reading was taken once a minute. After each trial the water was ...

84

Stirring will win, hands down, every time. This is why physicists need to talk to chemists once in a while. As Georg correctly remarks, the latent heat of vaporization of water is enormous - but he's wrong about waving the spoon; stirring is the champion here. Why? Temperature is really the average kinetic energy of the molecules in the bulk substance, ...

56

There's a lot of detail you could go into with regard to this question, as is done in the other answers and comments, but I think the answer itself is pretty simple. Imagine a surface that just barely surrounds your body, as if you shrink-wrapped a body in plastic. By the law of conservation of mass (valid in non-relativistic physics), the only way your body ...

47

Ice cubes have three distinct cooling effects: The cube, initially at sub-zero temperature, absorbs some heat to reach fusion point (0⁰C). The cube absorbs more heat to switch phase: it takes some energy to turn 1 kg of ice at 0⁰C into 1 kg of liquid water at 0⁰C. The water absorbs some heat to become warmer than 0⁰C. The three effects occur more or less ...

34

Essentially, losing of weight occurs by means of burning fuels precisely like your car does when it burns petrol and emits exhaust gases. The only difference is that for humans that fuel is to be found in the form of sugars. The fat is what you want to get ultimately rid off, of course, but sugars are more easily processed and so this is what you are ...

29

This is a very interesting question with a very interesting answer. The key lies in the reason for the stretchiness of the rubber band. Rubber is made of polymers (long chain molecules). When the elastic band is not stretched, these molecules are all tangled up with each other and have no particular direction to them, but when you stretch the elastic they ...

28

When you exercise, you "burn" more glucose, the simplified reaction for which (from Wikipedia) is: ${\rm C_6H_{12}O_6 + 6~O_2 → 6~CO_2 + 6~H_2O}$ So when you exhale, the carbon in the carbon dioxide, and the hydrogen and the oxygen in the water vapor, came from the glucose being burned, thereby removing that mass from the body.

27

I'll try to give an answer in purely classical thermodynamics. Summary Heat is a way of accounting for energy transfer between thermodynamic systems. Whatever energy is not transferred as work is transferred as heat. If you observe a thermodynamic process and calculate that system A lost $Q$ calories of heat, this means that if the environment around ...

27

One reason you might think $T$ should be measured in Joules is the idea that temperature is the average energy per degree of freedom in a system. However, this is only an approximation. That definition would correspond to something proportional to $\frac{U}{S}$ rather than $\frac{\partial U}{\partial S}$, which is the real definition. The approximation holds ...

23

It depends on what you mean by efficiency. Suppose you want to heat your house. An electric heater like you're considering would do this by converting electrical energy directly into heat. Pretty much all the electrical energy does get converted to heat, as you suggest. The energy used to get a certain amount of heat into the house is simply equal to ...

21

The gas molecules in your bottle of air aren't just sitting still, they're moving around in random directions. From memory, the speed of oxygen and nitrogen molecules at room temperature is around 500 meters per second. When the bottle is closed, the air molecules hit the walls and lid of the bottle and bounce back, so the air stays in the bottle. If you ...

21

If you have only one species of particles then working with $(\mu,p,T)$ ensemble does not make sense, as its thermodynamic potential is $0$. $$U = TS -pV + \mu N,$$ so the Legendre transformation in all of its variables (i.e. $S-T$, $V-(-p)$ and $N-\mu$) $$U[T,p,\mu] = U - TS + pV - \mu N$$ is always zero. The fact is called Gibbs-Duhem relation, i.e. $$0 ... 21 What a great question! And because anything that involves food is close to my heart I can answer with authority having done the experiments :-) There's a simple answer, a more complex answer and even an unexpected answer! The simple answer is that if you just want to boil off water you should leave the lid off. If you try the experiment of putting a known ... 20 How to cool a cup of coffee with the help of a spoon. Hmm... Empty the cup using the spoon, discarding the hot coffee. Strike the cup with the spoon, shattering it and forcing it to release the hot coffee. Drink the coffee with the spoon. Use the spoon to carve a cup-shaped hole in a large block of ice, put the cup in there. Put the spoon in the coffee, ... 20 Good question! Assuming the disc is uniform and isotropic (the same in different directions), the hole will expand in the same ratio as the metal. You can see this because the thermal expansion equation$$\mathrm{d} L = L\alpha\mathrm{d}T$$applies to all lengths associated with the metal, including the circumference of the hole, since the edge of the hole ... 20 David Zaslavski's answer is correct and complete. But I want to propose a different way to look at the problem. Think of the disc that was cut out, and imagine that you heat it too, exactly as you heat the plate. After heating, the disc will fit in exactly to the hole, just as if it was first heated and then cut out. Therefore, the hole will expand. 20 You are absolutely right about the dimensional analysis. The use of  \ln T  etc. is always a shorthand for  \ln \left(\frac{T}{T_0}\right)  which is okay to use if for some reason you don't care about  T_0 , i.e. because it cancels out or you are interested in the asymptotic behaviour only. In any expression where you have to take derivatives to get ... 19 With respect to the content in the cup, all Your hampering with the spoon is irrelevant. Cooling of a hot coffee is achieved by vaporisation of water. At temperatures between 100 and say 50 °C the vapor pressure is so big, that the heat carried away by convection of the hot (and much less dense than air!) vapor dominates all other heat transfer ... 19 Instead of a circular hole, let's think of a square hole. You can get a square hole two ways, you can cut it out of a complete sheet, or you can get one by cutting a sheet into 9 little squares and throwing away the center one. Since the 8 outer squares all get bigger when heat it, the inner square (the hole) also has to get bigger: Same thing happens ... 18 Its really pretty simple, the thermometer measures temperature, wind chill measures heat loss for a body warmer than the air. Wind makes more unheated air available to conduct heat away from a hot body, but with a body at air temperature no heat is being condicted away from the thermometer. If you asked a secondary question, when I put a thermometer outside, ... 17 Well, if you are only allowed to use a spoon, the fastest way to cool the coffee for drinking is to get a spoonful, blow on it, drink it from the spoon, take a next spoonful. Convection does wonders. If you are allowed a saucer instead of a spoon, pour a bit of coffee in the saucer, blow on it and drink it. 17 UPDATE: Below I am answering yes to the first question in the post (are the two kinds of entropy the same up to a constant). This has led to some confusion as both Matt and John gave answers saying "the answer is no", however I believe they are referring to the title "Does entropy measure extractable work?". Although the author uses the two interchangeably, ... 16 As others have pointed out, in metabolism you breathe in oxygen and exhale carbon dioxide with the net reaction being$$CH_2O + O_2 \to CO_2 + H_2O The carbon dioxide gets exhaled, and the water is lost through some combination of other things. Let's think about whether this is a reasonable way to explain weight loss. A breath is maybe one liter of ...

15

I can't believe the density or material of the spoon hasn't been considered. If the spoon is very dense you can take it and wave it in the air in a 15° arc and say, "Dear waiter, if you don't put some cold milk in my coffee I will hit you between the eyes with this abnormally dense spoon". On the other hand, if its made of gold or silver you hold it ...

15

Light diodes exist, and yet the 2nd law endures. In general, any perfect ratchet would allow you to violate the 2nd law. Since very few Nobel prizes have been awarded for perpetual motion machines, experimental evidence seems to suggest there is no such thing as a perfect ratchet. When confronted with any type of device that rectifies the flow of energy, ...

15

The theorem is called the noiseless coding theorem, and it is often proven in clunky ways in information theory books. The point of the theorem is to calculate the minimum number of bits per variable you need to encode the values of N identical random variables chosen from $1...K$ whose probabilities of having a value $i$ between $1$ and $K$ is $p_i$. The ...

15

Arnold Neumaier's comment about statistical mechanics is correct, but here's how you can prove it using just thermodynamics. Let's imagine two bodies at different temperatures in contact with one another. Let's say that body 1 transfers a small amount of heat $Q$ to body 2. Body 1's entropy changes by $-Q/T_1$, and body 2's entropy changes by $Q/T_2$, so ...

15

Nature has no preferences, and therefore entropy tends to increase. Sounds paradoxical? The point is that each microscopic state (describing the exact position and velocity of each atom in the system) is equally likely. However, what we typically observe is not a micro state, but a course-grained description corresponding to incredibly many micro states. ...

15

The two "no" answers you've already received are correct for all practical purposes. In real-world cases there can be a difference though. The difference depends on when the refrigerator decides to cycle on and cool. If the fridge cycles on a timer or based on heat energy then there will be a difference due to the added heat capacity. The outside of the ...

14

Statistical Mechanics is the theory of the physical behaviour of macroscopic systems starting from a knowledge of the microscopic forces between the constituent particles. The theory of the relations between various macroscopic observables such as temperature, volume, pressure, magnetization and polarization of a system is called thermodynamics. first ...

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