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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, 螖T=(25-20)oC = 5oC
Specific of water, C=4186 J /kgK

02

Explanation

Amount of heat added can be calculated as

Q=m c 螖T

Substitute values and calculate

Q=mc鈭�T=(0.2kg)脳(4186J/kg掳C)脳(5掳C)Q=4186J

4186 Joule is added to the system.

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Most popular questions from this chapter

According to a standard reference table, the R value of a 3.5 inch-thick vertical air space (within a wall) is 1.0 R in English units), while the R value of a 3.5-inch thickness of fiberglass batting is 10.9. Calculate the R value of a 3.5-inch thickness of still air, then discuss whether these two numbers are reasonable. (Hint: These reference values include the effects of convection.)

A 60-kghiker wishes to climb to the summit of Mt. Ogden, an ascent of5000vertical feet(1500m) .
aAssuming that she is 25%efficient at converting chemical energy from food into mechanical work, and that essentially all the mechanical work is used to climb vertically, roughly how many bowls of corn flakes (standard serving size 1ounce,100 kilocalories) should the hiker eat before setting out?
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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 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
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  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.

Suppose you have a gas containing hydrogen molecules and oxygen molecules, in thermal equilibrium. Which molecule are moving faster, on average? By what factor?

Measured heat capacities of solids and liquids are almost always at constant pressure, not constant volume. To see why, estimate the pressure needed to keep Vfixed as Tincreases, as follows.

(a) First imagine slightly increasing the temperature of a material at constant pressure. Write the change in volume,dV1, in terms of dTand the thermal expansion coefficient 尾introduced in Problem 1.7.

(b) Now imagine slightly compressing the material, holding its temperature fixed. Write the change in volume for this process, dV2, in terms of dPand the isothermal compressibility 魏T, defined as

魏T鈮�鈭�1V鈭�V鈭�PT

(c) Finally, imagine that you compress the material just enough in part (b) to offset the expansion in part (a). Then the ratio of dPtodTis equal to (鈭�P/鈭�T)V, since there is no net change in volume. Express this partial derivative in terms of 尾and魏T. Then express it more abstractly in terms of the partial derivatives used to define 尾and魏T. For the second expression you should obtain

鈭�P鈭�TV=鈭�(鈭�V/鈭�T)P(鈭�V/鈭�P)T

This result is actually a purely mathematical relation, true for any three quantities that are related in such a way that any two determine the third.

(d) Compute 尾,魏T,and(鈭�P/鈭�T)Vfor an ideal gas, and check that the three expressions satisfy the identity you found in part (c).

(e) For water at 25鈭�C,尾=2.57脳10鈭�4K鈭�1and魏T=4.52脳10鈭�10Pa鈭�1. Suppose you increase the temperature of some water from 20鈭�Cto30鈭�C. How much pressure must you apply to prevent it from expanding? Repeat the calculation for mercury, for which (at25鈭�C)尾=1.81脳10鈭�4K鈭�1and魏T=4.04脳10鈭�11Pa鈭�1

Given the choice, would you rather measure the heat capacities of these substances at constant vor at constant p?
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