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Chapter 1: Q. 1.27 (page 19)

Give an example of a process in which no heat is added to a system, but its temperature increases. Then give an example of the opposite: a process in which heat is added to a system but its temperature does not change.

Short Answer

Expert verified

No heat is added to a system, but its temperature increases : Heating a resister

a process in which heat is added to a system but its temperature does not change: Boiling water

Step by step solution

01

Given

No heat is added to a system, but its temperature increases and

A process in which heat is added to a system but its temperature does not change.

02

Explanation

Heat is defined as any flow of energy between two objects due to difference in temperature between them.
In thermodynamics work is defined as any transfer of energy into or out of system from surroundings.

Any process in which work is done on a body can raise the temperature even if no heat flows. The heating of resistor is a one of example which does work on the system from current flow in the resistor which is not because of the heat flow.
Opposite is also possible to add heat to a system without raising its temperature.
When water reaches its boiling point the temperature of water doesn't increase any further. The heat is used to vaporize water at a constant temperature.


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Most popular questions from this chapter

Make a rough estimate of the thermal conductivity of helium at room temperature. Discuss your result, explaining why it differs from the value for air.

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 βintroduced 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 κT, defined as

κT≡−1V∂V∂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 (∂P/∂T)V, since there is no net change in volume. Express this partial derivative in terms of βandκT. Then express it more abstractly in terms of the partial derivatives used to define βandκT. For the second expression you should obtain

∂P∂TV=−(∂V/∂T)P(∂V/∂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 β,κT,and(∂P/∂T)Vfor an ideal gas, and check that the three expressions satisfy the identity you found in part (c).

(e) For water at 25∘C,β=2.57×10−4K−1andκT=4.52×10−10Pa−1. Suppose you increase the temperature of some water from 20∘Cto30∘C. How much pressure must you apply to prevent it from expanding? Repeat the calculation for mercury, for which (at25∘C)β=1.81×10−4K−1andκT=4.04×10−11Pa−1

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

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.

Calculate the rate of heat conduction through a layer of still air that is1mmthick, with an area of 1m2, for a temperature difference of 20∘C.

Calculate the total thermal energy in a gram of lead at room temperature, assuming that none of the degrees of freedom are "frozen out" (this happens to be a good assumption in this case).
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