# 15.1 The first law of thermodynamics  (Page 7/10)

 Page 7 / 10

## Section summary

• The first law of thermodynamics is given as $\Delta U=Q-W$ , where $\Delta U$ is the change in internal energy of a system, $Q$ is the net heat transfer (the sum of all heat transfer into and out of the system), and $W$ is the net work done (the sum of all work done on or by the system).
• Both $Q$ and $W$ are energy in transit; only $\Delta U$ represents an independent quantity capable of being stored.
• The internal energy $U$ of a system depends only on the state of the system and not how it reached that state.
• Metabolism of living organisms, and photosynthesis of plants, are specialized types of heat transfer, doing work, and internal energy of systems.

## Conceptual questions

Describe the photo of the tea kettle at the beginning of this section in terms of heat transfer, work done, and internal energy. How is heat being transferred? What is the work done and what is doing it? How does the kettle maintain its internal energy?

The first law of thermodynamics and the conservation of energy, as discussed in Conservation of Energy , are clearly related. How do they differ in the types of energy considered?

Heat transfer $Q$ and work done $W$ are always energy in transit, whereas internal energy $U$ is energy stored in a system. Give an example of each type of energy, and state specifically how it is either in transit or resides in a system.

How do heat transfer and internal energy differ? In particular, which can be stored as such in a system and which cannot?

If you run down some stairs and stop, what happens to your kinetic energy and your initial gravitational potential energy?

Give an explanation of how food energy (calories) can be viewed as molecular potential energy (consistent with the atomic and molecular definition of internal energy).

Identify the type of energy transferred to your body in each of the following as either internal energy, heat transfer, or doing work: (a) basking in sunlight; (b) eating food; (c) riding an elevator to a higher floor.

## Problems&Exercises

What is the change in internal energy of a car if you put 12.0 gal of gasoline into its tank? The energy content of gasoline is $1\text{.}3×{\text{10}}^{8}\phantom{\rule{0.25em}{0ex}}\text{J/gal}$ . All other factors, such as the car's temperature, are constant.

$1\text{.}6×{\text{10}}^{9}\phantom{\rule{0.25em}{0ex}}\text{J}$

How much heat transfer occurs from a system, if its internal energy decreased by 150 J while it was doing 30.0 J of work?

A system does $1\text{.}\text{80}×{\text{10}}^{8}\phantom{\rule{0.25em}{0ex}}\text{J}$ of work while $7\text{.}\text{50}×{\text{10}}^{8}\phantom{\rule{0.25em}{0ex}}\text{J}$ of heat transfer occurs to the environment. What is the change in internal energy of the system assuming no other changes (such as in temperature or by the addition of fuel)?

$-9\text{.}\text{30}×{\text{10}}^{8}\phantom{\rule{0.25em}{0ex}}\text{J}$

What is the change in internal energy of a system which does $4\text{.}\text{50}×{\text{10}}^{5}\phantom{\rule{0.25em}{0ex}}\text{J}$ of work while $3\text{.}\text{00}×{\text{10}}^{6}\phantom{\rule{0.25em}{0ex}}\text{J}$ of heat transfer occurs into the system, and $8\text{.}\text{00}×{\text{10}}^{6}\phantom{\rule{0.25em}{0ex}}\text{J}$ of heat transfer occurs to the environment?

Suppose a woman does 500 J of work and 9500 J of heat transfer occurs into the environment in the process. (a) What is the decrease in her internal energy, assuming no change in temperature or consumption of food? (That is, there is no other energy transfer.) (b) What is her efficiency?

(a) $-1\text{.}0×{\text{10}}^{4}\phantom{\rule{0.25em}{0ex}}\text{J}$ , or $-2\text{.}\text{39 kcal}$

(b) 5.00%

(a) How much food energy will a man metabolize in the process of doing 35.0 kJ of work with an efficiency of 5.00%? (b) How much heat transfer occurs to the environment to keep his temperature constant? Explicitly show how you follow the steps in the Problem-Solving Strategy for thermodynamics found in Problem-Solving Strategies for Thermodynamics .

(a) What is the average metabolic rate in watts of a man who metabolizes 10,500 kJ of food energy in one day? (b) What is the maximum amount of work in joules he can do without breaking down fat, assuming a maximum efficiency of 20.0%? (c) Compare his work output with the daily output of a 187-W (0.250-horsepower) motor.

(a) 122 W

(b) $2\text{.}\text{10}×{\text{10}}^{6}\phantom{\rule{0.25em}{0ex}}\text{J}$

(c) Work done by the motor is $1\text{.}\text{61}×{\text{10}}^{7}\phantom{\rule{0.25em}{0ex}}\text{J}$ ;thus the motor produces 7.67 times the work done by the man

(a) How long will the energy in a 1470-kJ (350-kcal) cup of yogurt last in a woman doing work at the rate of 150 W with an efficiency of 20.0% (such as in leisurely climbing stairs)? (b) Does the time found in part (a) imply that it is easy to consume more food energy than you can reasonably expect to work off with exercise?

(a) A woman climbing the Washington Monument metabolizes $6\text{.}\text{00}×{\text{10}}^{2}\phantom{\rule{0.25em}{0ex}}\text{kJ}$ of food energy. If her efficiency is 18.0%, how much heat transfer occurs to the environment to keep her temperature constant? (b) Discuss the amount of heat transfer found in (a). Is it consistent with the fact that you quickly warm up when exercising?

(a) 492 kJ

(b) This amount of heat is consistent with the fact that you warm quickly when exercising. Since the body is inefficient, the excess heat produced must be dissipated through sweating, breathing, etc.

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