Ch $14$ Exercises

$14-1$: Heat as Energy Transfer:

$2.($I$)$ How much heat $($in joules$)$ is required to raise the temperature of $34\mathrm{.}0$ kg of water from $15C$ to $95C?$

$14-3$ and $14-4$: Specific Heat; Calorimetry:

$11.($II$)($a$)$ How much energy is required to bring a $1\mathrm{.}0-L$ pot of water at $20C$ to $100C?($b$)$ For how long could this amount of energy run a $60-W$ lightbulb?

$18.($II$)$ The heat capacity, $C,$ of an object is defined as the amount of heat needed to raise its temperature by $1C.$ Thus, to raise the temperature by $T$ requires heat $Q$ given by

$Q=CT$

$($a$)$ Write the heat capacity $C$ in terms of the specific heat, $c,$ of the material. $($b$)$ What is the heat capacity of $1\mathrm{.}0$ kg of water? $($c$)$ Of $45$ kg of water?

$14-5$: Latent Heat:

$26.($II$)$ A $28-g$ ice cube at its melting point is dropped into an insulated container of liquid nitrogen. How much nitrogen evaporates if it is at its boiling point of $77$ K and has a latent heat of vaporization of $200k\frac{J}{k}g?$ Assume for simplicity that the specific heat of ice is a constant and is equal to its value near its melting point.

$31.($II$)$ A $55-g$ bullet traveling at $250\frac{m}{s}$ penetrates a block of ice at $0C$ and comes to rest within the ice. Assuming that the temperature of the bullet doesn't change appreciably, how much ice is melted as a result of the collision?

$14-6$ through $14-8$: Conduction, Convection, Radiation:

$32.($I$)$ One end of a $56-cm-$long copper rod with a diameter of $2\mathrm{.}0$ cm is kept at $460C,$ and the other is immersed in water at $22C.$ Calculate the heat conduction rate along the rod.

$35.($II$)$ Heat conduction to skin. Suppose $150$ W of heat flows by conduction from the blood capillaries beneath the skin to the body's surface area of $1\mathrm{.}5m^2.$ If the temperature difference is $0\mathrm{.}50C,$ estimate the average distance of capillaries below the skin surface.

General Problems:

$41.($a$)$ Estimate the total power radiated into space by the Sun, assuming it to be a perfect emitter at $T=5500K.$ The Sun's radius is $7\mathrm{.}0{10}^{8}m.($b$)$ From this, determine the power per unit area arriving at the Earth, $1\mathrm{.}5{10}^{11}m$ away $($Fig$.14-20).$

FIGURE $14-20$

$r=1\mathrm{.}5{10}^{11}m$

Problem $41.$

$50.$ A $2\mathrm{.}3-kg$ lead ball is placed in a $2\mathrm{.}5-L$ insulated pail of water initially at $20\mathrm{.}0C.$ If the final temperature of the water$-$lead combination is $32\mathrm{.}0C,$ what was the initial temperature of the lead ball?

$55.$ The temperature within the Earth's crust increases about $1\mathrm{.}0C$ for each $30$ m of depth. The thermal conductivity of the crust is $0\mathrm{.}80\frac{J}{s}*C*m.($a$)$ Determine the heat transferred from the interior to the surface for the entire Earth in $1\mathrm{.}0$ h $.($b$)$ Compare this heat to the $1000\frac{W}{m^2}$ that reaches the Earth's surface in $1\mathrm{.}0$ h from the Sun.

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