Exam 14: Heat

Two identical objects are placed in a room with a temperature of $20 ^ { \circ } \mathrm { C }$ Object A has a temperature of $50 ^ { \circ } \mathrm { C }$ while object B has a temperature of $90 ^ { \circ } \mathrm { C }$ What is the ratio of the net power emitted by object B to the power emitted by object A?

A 6.5-g iron meteor hits the earth at a speed of 295 m/s. If its kinetic energy is entirely converted to heat in the meteor, by how much will its temperature rise? The specific heat of iron is $113 \mathrm { cal } / \mathrm { kg } \text {. }$ $\mathrm { C } ^ { \circ }$ and 1 cal=4.186 J

A glass beaker of unknown mass contains 74.0 ml of water. The system absorbs 2000.0 cal of heat and the temperature rises $20.0 ^ { \circ } \mathrm { C }$ as a result. What is the mass of the beaker? The specific heat of glass is $0.18 \mathrm { cal } / \mathrm { g } \cdot { } ^ { \circ } \mathrm { C }$ and that of water is $1.0 \mathrm { cal } / \mathrm { g } \cdot \mathrm { C } ^ { \circ }$

The melting point of aluminum is $660 ^ { \circ } \mathrm { C }$ its latent heat of fusion is $4.00 \times 10 ^ { 5 } \mathrm {~J} / \mathrm { kg }$ and its specific heat is $900 \mathrm {~J} / \mathrm { kg } \cdot \mathrm { K }$ If 300 kJ of heat are added to 442 g of aluminum at $100 ^ { \circ } \mathrm { C }$ what is the final state of the system? That is, how much is liquid, how much is solid, and what is its temperature?

A concrete wall of a cold storage room measures 3.0 m high, 5.0 m wide, and 20 cm thick. The inside wall is to be covered by a layer of wood in order to reduce the rate of heat flow through the wall by 90 percent. The inner surface of the wooden wall is maintained at $- 10 ^ { \circ } \mathrm { C }$ and the outer surface of the concrete wall is at $20 ^ { \circ } \mathrm { C }$ The thermal conductivities of concrete and wood are $0.80$ $\mathrm { W } / \mathrm { m } \cdot \mathrm { K }$ (concrete) and 0.040 $\mathrm { W } / \mathrm { m } \cdot \mathrm { K } \text { (wood) }$ What is the temperature difference across the layer of wood?

A container of 114.0 g of water is heated using 67.0 W of power, with perfect efficiency. How long will it take to raise the temperature of the water from $15 ^ { \circ } \mathrm { C } \text { to } 25 ^ { \circ } \mathrm { C } \text { ? }$ The specific heat capacity of the container is negligible, and the specific heat capacity of water is $4.186 \times 10 ^ { 3 } \mathrm {~J} / \mathrm { kg } \cdot \mathrm { C }$

Two metal rods, one silver and the other gold, are attached to each other end-to-end. The free end of the silver rod is immersed in a steam chamber at $100 ^ { \circ } \mathrm { C }$ and the free end of the gold rod in an ice water bath at $0 ^ { \circ } \mathrm { C }$ The rods are both 5.0 cm long and have a square cross-section that is 2.0 cm on a side. No heat is exchanged between the rods and their surroundings, except at the ends. What is the temperature at the point where the two rods are in contact with one another? The thermal conductivity of silver is 417 $\mathrm { W } / \mathrm { m } \cdot \mathrm { K } .$ and that of gold is 291 $\mathrm { W } / \mathrm { m } \cdot \mathrm { K } .$

A jogger is running outdoors on a cold day when the temperature is $- 20.0 ^ { \circ } \mathrm { C }$ she is breathing at the rate of 25 breaths per minute, and each time she breathes in she inhales $0.00450 \mathrm {~m} ^ { 3 }$ of air. How much heat does she lose from breathing during 20.0 minutes of jogging if the air in her lungs is heated to her body temperature of $37.0 ^ { \circ } \mathrm { C }$ before it is exhaled? The specific heat of air is $1020 \mathrm {~J} / \mathrm { kg }$ K and the density of air under typical conditions is $1.29 \mathrm {~kg} / \mathrm { m } ^ { 3 }$

Two experimental runs are performed to determine the calorimetric properties of an alcohol which has a melting point of $- 10.0 ^ { \circ } \mathrm { C } .$ In the first run, a 200-g cube of frozen alcohol, at the melting point, is added to 300 g of water at $20.0 ^ { \circ } \mathrm { C }$ in a styrofoam container. When thermal equilibrium is reached, the alcohol-water solution is at a temperature of $5.0 ^ { \circ } \mathrm { C }$ In the second run, an identical cube of alcohol is added to 500 g of water at $20.0 ^ { \circ } \mathrm { C }$ and the temperature at thermal equilibrium is $10.0 ^ { \circ } \mathrm { C }$ The specific heat capacity of water is $4190 \mathrm {~J} / \mathrm { kg } \cdot \mathrm { K } .$ Assume no heat is exchanged with the styrofoam container and the surroundings. What is the heat of fusion of the alcohol?

A piece of iron of mass 0.12 kg is taken from an oven where its temperature is $336 ^ { \circ } \mathrm { C }$ and quickly placed in an insulated copper can that contains 0.20 kg of water. The copper can has mass 0.50 kg, and it and the water in it are originally at a temperature of $20 ^ { \circ } \mathrm { C }$ Calculate the final temperature of the system, assuming no heat is lost to the surroundings. Use the following specific heats: $4190 \mathrm {~J} / \mathrm { kg } \cdot \mathrm { C } ^ { \circ } \text { (water), } 470 \mathrm {~J} / \mathrm { kg } \cdot \mathrm { C } ^ { \circ } \text { (iron), }$ and $390 \mathrm {~J} / \mathrm { kg } \cdot \mathrm { C } ^ { \circ } \text { (copper). }$

The cylindrical filament in a light bulb has a diameter of 0.050 mm, an emissivity of 1.0 , and a temperature of $3000 ^ { \circ } \mathrm { C } \text {. }$ How long should the filament be in order to radiate 60 W of power? $( \sigma =$ $\left. 5.67 \times 10 ^ { - 8 } \mathrm {~W} / \mathrm { m } ^ { 2 } \cdot \mathrm { K } ^ { 4 } \right)$

A 0.600-kg piece of metal X is heated to $100 ^ { \circ } \mathrm { C }$ and placed in an aluminum can of mass 0.200-kg which contains $0.500 \mathrm {~kg}$ of water initially at $17.3 ^ { \circ } \mathrm { C }$ The final equilibrium temperature of the mixture is $20.2 ^ { \circ } \mathrm { C }$ What is the specific heat of metal X? The specific heats of water and aluminum are 4186 $\mathrm { J } / \mathrm { kg } \cdot \mathrm { K }$ (water) and 910 $\mathrm { J } / \mathrm { kg } \cdot \mathrm { K } \text { (aluminum). }$

A substance has a melting point of $20 ^ { \circ } \mathrm { C }$ and a heat of fusion of $3.6 \times 10 ^ { 4 } \mathrm {~J} / \mathrm { kg }$ The boiling point is $150 ^ { \circ } \mathrm { C }$ and the heat of vaporization is $7.2 \times 10 ^ { 4 } \mathrm {~J} / \mathrm { kg }$ at a pressure of one atmosphere. The specific heats for the solid, liquid, and gaseous phases are $600 \mathrm {~J} / \mathrm { kg } \cdot \mathrm { K } \text { (solid), } 1000 \mathrm {~J} / \mathrm { kg } \cdot \mathrm { K } \text { (liquid), and } 400$ $\mathrm { J } / \mathrm { kg } \cdot \mathrm { K } \text { (gaseous). }$ How much heat is given up by 2.80 kg of this substance when it is cooled from $170 ^ { \circ } \mathrm { C } \text { to } 86 ^ { \circ } \mathrm { C }$ at a pressure of one atmosphere?

A beaker of negligible heat capacity contains 456 g of ice at $- 25.0 ^ { \circ } \mathrm { C }$ A lab technician begins to supply heat to the container at the rate of 1000 J/min. How long after starting will the ice begin to melt, assuming all of the ice has the same temperature? The specific heat of ice is $2090 \mathrm {~J} / \mathrm { kg } \cdot \mathrm { K }$ and the latent heat of fusion of water is $33.5 \times 10 ^ { 4 } \mathrm {~J} / \mathrm { kg }$

A carpenter is driving a 15.0-g steel nail into a board. His 1.00-kg hammer is moving at 8.50 m/s when it strikes the nail. Half of the kinetic energy of the hammer is transformed into heat in the nail and does not flow out of the nail. What is the increase in temperature of the nail after the three blows that the carpenter needs to drive the nail in completely? The specific heat of steel is 448 J/kg . K

A 5.00-g lead BB moving at 44.0 m/s penetrates a wood block and comes to rest inside the block. If half of its kinetic energy is absorbed by the BB, what is the change in the temperature of the BB? The specific heat of lead is 128 $\mathrm { J } / \mathrm { kg } \cdot \mathrm { K } .$

If 50 g of lead (of specific heat $\left. 0.11 \mathrm { kcal } / \mathrm { kg } \cdot \mathrm { C } ^ { \circ } \right)$ at $100 ^ { \circ } \mathrm { C }$ is put into 75 g of water (of specific heat $\left. 1.0 \mathrm { kcal } / \mathrm { kg } \cdot \mathrm { C } ^ { \circ } \right) \text { at } 0 ^ { \circ } \mathrm { C }$ What is the final temperature of the mixture?

A giant star radiates energy at the rate of $3.0 \times 10 ^ { 30 } \mathrm {~W}$ and its surface temperature has been measured to be 3000 K. Assuming that it is a perfect emitter, what is the radius of this star? $( \sigma =$ $\left. 5.67 \times 10 ^ { - 8 } \mathrm {~W} / \mathrm { m } ^ { 2 } \cdot \mathrm { K } ^ { 4 } \right)$

In a flask, 114.0 g of water is heated using 67.0 W of power, with perfect efficiency. How long will it take to raise the temperature of the water from $15 ^ { \circ } \mathrm { C } \text { to } 25 ^ { \circ } \mathrm { C } ?$ The specific heat of water is 4186 $\mathrm { J } / \mathrm { kg } \cdot \mathrm { K } .$

In an electric furnace used for refining steel, the temperature is monitored by measuring the radiant power emitted through a small hole in the wall of the furnace, of area $0.5 \mathrm {~cm} ^ { 2 }$ This hole acts like a perfect blackbody radiator having the same temperature as the interior of the furnace. If the temperature of the furnace (and therefore of the hole) is to be maintained at $1650 ^ { \circ } \mathrm { C } \text {, }$ how much power will the hole radiate?