Find the temperature drop across the epidermis (the outer layer of skin) under these conditions: the rate of heat flow via conduction through a 10.0 $\mathrm { cm } ^ { 2 }$ area of the epidermis is 50 mW; the epidermis is 2.00 mm thick and has thermal conductivity 0.45 $\mathrm { W } / ( \mathrm { m } \cdot \mathrm { K } )$.

In an emergency, it is sometimes the practice of medical professionals to immerse a patient who suffers from heat stroke in an ice bath, a mixture of ice and water in equilibrium at $0 ^ { \circ } \mathrm { C }$, in order to reduce body temperature is $40.8 ^ { \circ } \mathrm { C }$ must have her temperature reduced to the normal range, how much heat must be removed? (b) If she is placed in a bath containing 7.5 kg of ice, will there be ice remaining in the bath when her body temperature is $37.0 ^ { \circ } \mathrm { C } ?$ If so, how much? If not, what will the final water temperature be?

A high jumper of mass 60.0 kg consumes a meal of

$$3.00 \times 10 ^ { 3 }$$

kcal prior to a jump. If 3.3% of the energy from the food could be converted to gravitational potential energy in a single jump, how high could the athlete jump?

Use an analysis-of-variance approach to test the hypothesis that \beta_{1}=0 against the alternative hypothesis \beta_{1} \neq 0 in Exercise 11.5 on page 398 at the 0.05 level of significance.

Find the LCM of $16c^6$ and $24c^3.$

Imagine that 501 people are present in a movie theater of volume

$$8.00 \times 10 ^ { 3 } \mathrm { m } ^ { 3 }$$

that is sealed shut so no air can escape. Each person gives off heat at an average rate of 110 W. By how much will the temperature of the air have increased during a 2.0 h movie? The initial pressure is

$$1.01 \times 10 ^ { 5 }$$

Pa and the initial temperature is

$$20.0 ^ { \circ } \mathrm { C }$$

. Assume that all the heat output of the people goes into heating the air (a diatomic gas).

An 83 kg man eats a banana of energy content 418 kJ (100 kcal). If all of the energy from the banana is converted into kinetic energy of the man, how fast is he moving, assuming he starts from rest?

A person is doing leg lifts with 3.0 kg ankle weights. She is sitting in a chair with her legs bent at a right angle initially. The quadriceps muscles are attached to the patella via a tendon; the patella is connected to the tibia by me patellar tendon, which attaches to bone 10.0 cm below the knee joint. Assume that the tendon pulls at an angle of

$$20.0 ^ { \circ }$$

with respect to the lower leg, regardless of the position of the lower leg. The lower leg has a mass of 5.0 kg, and its center of gravity is 22 cm below the knee. The ankle weight is 41 cm from the knee. If the person lifts one leg, find the force exerted by the patellar tendon to hold the leg at an angle of (a)

$$30.0 ^ { \circ }$$

and (b)

$$90.0 ^ { \circ }$$

with respect to the vertical.

A person is doing leg lifts with 3.00 kg ankle weights. The lower leg itself has a mass of 5.00 kg. When the leg is held still at an angle of $30.0 ^ { \circ }$ with respect to the horizontal, the patellar tendor pulls on the tibia with a force of 337 N at an angle of $30.0 ^ { \circ }$ with respect to the horizontal, the patellar tendon pulls on the tibia with a force of 337 N at an angle of $20.0 ^ { \circ }$ with respect to the lower leg. Find the magnitude and direction of the force exerted on the tibia by the femur, assuming it is the only other significant force acting on the lower leg.

Women often experience back pain when they are pregnant. Suppose a woman's mass before pregnancy is 68 kg and her center of mass when standing is located directly above the hips. By the thirty-fourth week of pregnancy, she has gained 8.0 kg (the combined mass of the fetus, the placenta, and the amniotic fluid). The center of mass of this 8.0 kg is 18 cm in front of the hips. If she hasn't changed her posture, how far in front of the hips is her center of mass? [Women have three wedge-shaped lumbar vertebrae, whereas man have only two. This evolutionary adaptation permits a greater curvature of the lumbar spine to keep a pregnant woman's $\mathrm { CM }$ above the hips.

Use the x- and y-intercepts to graph each linear equation.

$$5x = 3y - 15$$

Before going in for his annual physical, a 70.0-kg man whose body temperature is $37.0^{\circ} \mathrm{C}$ consumes an entire 0.355-L can of a soft drink (mostly water) at $12.0^{\circ} \mathrm{C}$.

Is the change in his body temperature great enough to be measured by a medical thermometer?

In very cold weather a significant mechanism for heat loss by the human body is energy expended in warming the air taken into the lungs with each breath. (a) On a cold winter day when the temperature is $-20^{\circ} C$, what amount of heat is needed to warm to body temperature $\left(37^{\circ} \mathrm{C}\right)$ the 0.50 L of air exchanged with each breath? Assume that the specific heat of air is $1020 \mathrm{J} / \mathrm{kg} \cdot \mathrm{K}$ and that 1.0 L of air has mass $1.3 \times 10^{-3} \mathrm{kg}$. (b) How much heat is lost per hour if the respiration rate is 20 breaths per minute?

The amount of food energy per day required by a person resting under standard conditions is called the basal metabolic rate (BMR). (a) To generate 1 kcal, Jermaine's body needs approximately 0.010 mol of oxygen. If Jermaine's net intake of oxygen through breathing is 0.015 mol/min while he is resting, what is his BMR in kcal/day? (b) If Jermaine fasts for 24 h, how many pounds of fat does he lose? Assume that only fat is consumed. Each gram of fat consumed generates 9.3 kcal.