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Chapter 1: Q.1.28 (page 20)

Estimate how long it should take to bring a cup of water to boiling temperature in a typical 600-wattmicrowave oven, assuming that all the energy ends up in the water. (Assume any reasonable initial temperature for the water.) Explain why no heat is involved in this process.

Short Answer

Expert verified

Time is taken to boil2.616 minutes to raise the 20mlwater fromlocalid="1648467354265" 10°Cto100°C.

Step by step solution

01

Step 1. Finding Amount of heat.

Consider a mug filled with250mLcold10°Cwater in a 600wattmicrowave. To achieve the boiling point, So must raise the temperature by90˚C.

Q=mCΔT

m=Water mass.

C=Specific heat C=4.186J/g·C∘

ΔT=90°Temp

Therefore,

Q=250×4.186×90=94185J.

02

Step 2. Boiling time.

The Power

P=Qt→t=QP

Insert Qand Pvalues.

t=94185600=156.975s=2.616min.

Normally, heat is transferred from the hotter to the colder object. However, because there is no hot item in our scenario, the heat is transported to the mug via an electromagnetic wave generated by the magnetron.

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Most popular questions from this chapter

Problem 1.36. In the course of pumping up a bicycle tire, a liter of air at atmospheric pressure is compressed adiabatically to a pressure of 7 atm. (Air is mostly diatomic nitrogen and oxygen.)

(a) What is the final volume of this air after compression?

(b) How much work is done in compressing the air?

(c) If the temperature of the air is initially300K , what is the temperature after compression?

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 Δtis role="math" localid="1651729685802" PAΔt/(2mvx¯), 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¯)1/2, where the bar now represents an average overall molecule in the gas. Show that (vx2¯)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=−A2VkTmN
    Solve this equation (assuming constant temperature) to obtain a formula of the form N(t)=N(0)e−t/r, where ris the “characteristic time” 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’s 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.

Problem 1.49. Consider the combustion of one mole of H2with1/2 mole ofO2 under standard conditions, as discussed in the text. How much of the heat energy produced comes from a decrease in the internal energy of the system, and how much comes from work done by the collapsing atmosphere? (Treat the volume of the liquid water as negligible.)

A battery is connected in series to a resistor, which is immersed in water (to prepare a nice hot cup of tea). Would you classify the flow of energy from the battery to the resistor as "heat" or "work"? What about the flow of energy from the resistor to the water?

Consider a narrow pipe filled with fluid, where the concentration of a specific type of molecule varies only along its length (in the x direction). Fick's second law is derived by considering the flux of these particles from both directions into a short segment∆x

∂n∂t=D∂2n∂x2
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