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Chapter 1: 1.4. (page 5)

Does it ever make sense to say that one object is "twice as hot" as another? Does it matter whether one is referring to Celsius or Kelvin temperatures? Explain.

Short Answer

Expert verified

No, the statement according to physics is wrong. And the Celsius and Kelvin scales cannot give a good comparison of temperatures..

Step by step solution

01

differences between heat and temperature.

There are two distinct terms- "heat" and "temperature". heat is a term for transfer of energy from one point to another from higher temperature to the lower temperature; whereas temperature is the measure of degree of hotness or coldness of the object.

02

Comparison of heat and reading it in terms of temperature

Hence one can say that object has twice the temperature than the other, since the quantities has a clear description on how they are measured

03

The values of absolute zero of Celsius and Fahrenheit scales.

If one object was 400C and another 800C then in Celsius scale one is twice the other. But if we convert into Fahrenheit scales those temperatures come to 313.15K and 353.15K. So in this respect we can say that second object is not twice the temperature of the first. Hence we can explain the contradiction that these scales cannot be measured in the same segment.

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Most popular questions from this chapter

Your 200 g cup of tea is boiling-hot. About how much ice should you add to bring it down to a comfortable sipping temperature of 65掳C? (Assume that the ice is initially 65掳C. The specific heat capacity of ice isrole="math" localid="1650146844935" 0.5cal/g掳C.

Consider a uniform rod of material whose temperature varies only along its length, in the xdirection. By considering the heat flowing from both directions into a small segment of length 螖x

derive the heat equation,

鈭�T鈭�t=K鈭�2T鈭�x2

where K=kt/c蚁i, cis the specific heat of the material, and 蚁is its density. (Assume that the only motion of energy is heat conduction within the rod; no energy enters or leaves along the sides.) Assuming that Kis independent of temperature, show that a solution of the heat equation is

T(x,t)=T0+Ate鈭�x2/4Kt,

where T0is a constant background temperature and Ais any constant. Sketch (or use a computer to plot) this solution as a function of x, for several values of t. Interpret this solution physically, and discuss in some detail how energy spreads through the rod as time passes.

If you poke a hole in a container full of gas, the gas will start leaking out. In this problem, you will make a rough estimate of the rate at which gas escapes through a hole. (This process is called effusion, at least when the hole is sufficiently small.)

  1. Consider a small portion (area = A) of the inside wall of a container full of gas. Show that the number of molecules colliding with this surface in a time interval 螖tis role="math" localid="1651729685802" PA螖t/(2mvx炉), where width="12" height="19" role="math">Pis the pressure, is the average molecular mass, and vxis the average xvelocity of those molecules that collide with the wall.
  2. It's not easy to calculate vx, but a good enough approximation is (vx2炉)1/2, where the bar now represents an average overall molecule in the gas. Show that (vx2炉)1/2=kT/m.
  3. If we now take away this small part of the wall of the container, the molecules that would have collided with it will instead escape through the hole. Assuming that nothing enters through the hole, show that the number Nof molecules inside the container as a function of time is governed by the differential equation
    dNdt=鈭�A2VkTmN
    Solve this equation (assuming constant temperature) to obtain a formula of the form N(t)=N(0)e鈭�t/r, where ris the 鈥渃haracteristic time鈥� for N(and P) to drop by a factor of e.
  4. Calculate the characteristic time for gas to escape from a 1-liter container punctured by a 1-mm2? hole.
  5. Your bicycle tire has a slow leak so that it goes flat within about an hour after being inflated. Roughly how big is the hole? (Use any reasonable estimate for the volume of the tire.)
  6. In Jules Verne鈥檚 Around the Moon, the space travelers dispose of a dog's corpse by quickly opening a window, tossing it out, and closing the window. Do you think they can do this quickly enough to prevent a significant amount of air from escaping? Justify your answer with some rough estimates and calculations.

When the temperature of liquid mercury increases by one degree Celsius (or one kelvin), its volume increases by one part in 550,000 . The fractional increase in volume per unit change in temperature (when the pressure is held fixed) is called the thermal expansion coefficient, 尾 :
尾鈮�螖V/V螖T
(where V is volume, T is temperature, and 螖 signifies a change, which in this case should really be infinitesimal if 尾 is to be well defined). So for mercury, 尾 =1 / 550,000 K-1=1.81 x 10-4 K-1. (The exact value varies with temperature, but between 0oC and 200oC the variation is less than 1 %.)
(a) Get a mercury thermometer, estimate the size of the bulb at the bottom, and then estimate what the inside diameter of the tube has to be in order for the thermometer to work as required. Assume that the thermal expansion of the glass is negligible.
(b) The thermal expansion coefficient of water varies significantly with temperature: It is 7.5 x 10 -4 K-1 at 100oC, but decreases as the temperature is lowered until it becomes zero at 4oC. Below 4oC it is slightly negative, reaching a value of -0.68 x 10-4K-1 at 0oC. (This behavior is related to the fact that ice is less dense than water.) With this behavior in mind, imagine the process of a lake freezing over, and discuss in some detail how this process would be different if the thermal expansion coefficient of water were always positive.

The Fahrenheit temperature scale is defined so that ice melts at 320 F and water boils at 2120 F.

(a) Derive the formula for converting from Fahrenheit to Celsius and back

(b) What is absolute zero on the Fahrenheit scale?
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