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Chapter 1: Q. 1.29 (page 20)

A cup containing 200g of water is sitting on your dining room table. After carefully measuring its temperature to be 20oC, you leave the room. Returning ten minutes later, you measure its temperature again and find that it is now 25oC. What can you conclude about the amount of heat added to the water? (Hint: This is a trick question.)

Short Answer

Expert verified

Amount of heat added is 4186 J.

Step by step solution

01

Given information

Mass of water, m=200 g = 0.2 kg
Difference in temperature, ΔT=(25-20)oC = 5oC
Specific of water, C=4186 J /kgK

02

Explanation

Amount of heat added can be calculated as

Q=m c ΔT

Substitute values and calculate

Q=mc∆T=(0.2kg)×(4186J/kg°C)×(5°C)Q=4186J

4186 Joule is added to the system.

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Most popular questions from this chapter

When you're sick with a fever and you take your temperature with a thermometer, approximately what is the relaxation time?

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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.)

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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
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  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.)
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Imagine some helium in a cylinder with an initial volume of 1 liter and an initial pressure of 1 atm. Somehow the helium is made to expand to a final volume of 3 liters, in such a way that its pressure rises in direct proportion to its volume.

  1. Sketch a graph of pressure vs. volume for this process.
  2. Calculate the work done on the gas during this process, assuming that there are no “other” types of work being done.
  3. Calculate the change in the helium’s energy content during this process.
  4. Calculate the amount of heat added to or removed from the helium during this process.
  5. Describe what you might do to cause the pressure to rise as the helium expands.
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