Exam 14: Heat

What is the net power that a person with surface area of $1.20 \mathrm {~m} ^ { 2 }$ radiates if his emissivity is 0.895 , his skin temperature is $27 ^ { \circ } \mathrm { C }$ and he is in a room that is at a temperature of $17 ^ { \circ } \mathrm { C } ?$ $\left( \sigma = 5.67 \times 10 ^ { - 8 } \right.$ $\left. \mathrm { W } / \mathrm { m } ^ { 2 } \cdot \mathrm { K } ^ { 4 } \right)$

A lab student drops a 400.0-g piece of metal at $120.0 ^ { \circ } \mathrm { C }$ into a cup containing 450.0 g of water at $15.0 ^ { \circ } \mathrm { C }$ After waiting for a few minutes, the student measures that the final temperature of the system is $40.0 ^ { \circ } \mathrm { C }$ What is the specific heat of the metal, assuming that no significant heat is exchanged with the surroundings or the cup? The specific heat of water is $4186 \mathrm {~J} / \mathrm { kg } \cdot \mathrm { K } .$

A 771.0-kg copper bar is put into a smelter for melting. The initial temperature of the copper is 300.0 K. How much heat must the smelter produce to completely melt the copper bar? The specific heat for copper is $386 \mathrm {~J} / \mathrm { kg } \cdot \mathrm { K }$ the heat of fusion for copper is 205,000 J/kg, and its melting point is 1357 K.

The radius of a star is $6.95 \times 10 ^ { 8 } \mathrm {~m}$ and its rate of radiation has been measured to be $5.32 \times 10 ^ { 26 }$ W. Assuming that it is a perfect emitter, what is the temperature of the surface of this star? $( \sigma =$ $\left. 5.67 \times 10 ^ { - 8 } \mathrm {~W} / \mathrm { m } ^ { 2 } \cdot \mathrm { K } ^ { 4 } \right)$

A machine part consists of 0.10 kg of iron (of specific heat 470 $\mathrm { J } / \mathrm { kg } \cdot \mathrm { K }$ ) and 0.16 kg of copper (of specific heat 390 $\mathrm { J } / \mathrm { Kg } \cdot \mathrm { K } )$ How much heat must be added to the gear to raise its temperature from $18 ^ { \circ } \mathrm { C } \text { to } 53 ^ { \circ } \mathrm { C } ?$

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. How much total heat flows through the two rods each minute? 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 window glass that is 0.5 cm thick has dimensions of 3 m by 1.5 m. The thermal conductivity of this glass is 0.8 $\mathrm { W } / \mathrm { m } \cdot \mathrm { K }$ If the outside surface of the glass is at $- 10 ^ { \circ } \mathrm { C }$ and the inside surface is at $20 ^ { \circ } \mathrm { C }$ how much heat flows through the window in every hour?

A 360-g metal container, insulated on the outside, holds 180.0 g of water in thermal equilibrium at $22.0 ^ { \circ } \mathrm { C }$ A 24.0-g ice cube, at the melting point, is dropped into the water, and when thermal equilibrium is reached the temperature is $15.0 ^ { \circ } \mathrm { C }$ Assume there is no heat exchange with the surroundings. For water, the specific heat capacity is $4190 \mathrm {~J} / \mathrm { kg } \cdot \mathrm { K }$ and the heat of fusion is $3.34 \times$ $10 ^ { 5 } \mathrm {~J} / \mathrm { kg }$ What is the specific heat capacity of the metal of the container?

A 200-L electric water heater uses 2.0 kW. Assuming no heat loss, how many hours would it take to heat the water in this tank from $23 ^ { \circ } \mathrm { C } \text { to } 75 ^ { \circ } \mathrm { C } \text { ? }$ The specific heat of water is $4186 \mathrm {~J} / \mathrm { kg } \cdot \mathrm { K }$ and its density is $1000 \mathrm {~kg} / \mathrm { m } ^ { 3 }$

Two experimental runs are performed to determine the calorimetric properties of an alcohol which has a melting point of $- 10 ^ { \circ } \mathrm { C }$ In the first run, a 200-g cube of frozen alcohol, at the melting point, is added to 300 g of water at $20 ^ { \circ } \mathrm { C }$ in a styrofoam container. When thermal equilibrium is reached, the alcohol-water solution is at a temperature of $5 ^ { \circ } \mathrm { C }$ In the second run, an identical cube of alcohol is added to 500 g of water at $20 ^ { \circ } \mathrm { C }$ and the temperature at thermal equilibrium is $10 ^ { \circ } \mathrm { C }$ 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 specific heat capacity of the alcohol?

If you add 1.33 MJ of heat to 500 g of water at $50 ^ { \circ } \mathrm { C }$ in a sealed container, what is the final temperature of the steam? The latent heat of vaporization of water is $22.6 \times 10 ^ { 5 } \mathrm {~J} / \mathrm { kg }$ heat of steam is $2010 \mathrm {~J} / \mathrm { kg } \cdot \mathrm { K } _ { 1 }$ and the specific heat of water is $4186 \mathrm {~J} / \mathrm { kq } \cdot \mathrm { K }$ the specific

A 44.0-g block of ice at $- 15.0 ^ { \circ } \mathrm { C }$ is dropped into a calorimeter (of neglible heat capacity) containing 100 g of water at $5.0 ^ { \circ } \mathrm { C }$ When equilibrium is reached, how much of the ice will have melted? The specific heat of ice is $2090 \mathrm {~J} / \mathrm { kg } \cdot \mathrm { K }$ that of water is $4186 \mathrm {~J} / \mathrm { kg } \cdot \mathrm { K }$ and the latent heat of fusion of water is $33.5 \times 10 ^ { 4 } \mathrm {~J} / \mathrm { kg }$

The thermal conductivity of aluminum is twice that of brass. Two rods (one aluminum and the other brass) of the same length and cross-sectional area are joined together end to end. The free end of the brass rod is maintained at $0 ^ { \circ } \mathrm { C }$ and the free end of the aluminum rod is maintained at $200 ^ { \circ } \mathrm { C }$ If no heat escapes from the sides of the rods, what is the temperature at the place where the two rods are joined together?

How much power does a sphere with a radius of 10 cm radiate into empty space if is has an emissivity of 1.0 and is kept at a temperature of 400 K? $\left( \sigma = 5.67 \times 10 ^ { - 8 } \mathrm {~W} / \mathrm { m } ^ { 2 } \cdot \mathrm { K } ^ { 4 } \right)$

A heat-conducting rod that is wrapped in insulation is constructed with a 0.15-m length of alloy A and a 0.40-m length of alloy B , joined end-to-end. Both pieces have cross-sectional areas of 0.0020 $\mathrm { m } ^ { 2 }$ The thermal conductivity of alloy B is known to be 1.8 times as great as that for alloy A. The end of the rod in alloy A is maintained at a temperature of $10 ^ { \circ } \mathrm { C }$ and the other end of the rod is maintained at an unknown temperature. When steady state flow has been established, the temperature at the junction of the alloys is measured to be $40 ^ { \circ } \mathrm { C } ,$ and the rate of heat flow in the rod is measured at 56 W. What is the temperature of the end of the rod in alloy B?

A heat-conducting rod, 0.90 m long and wrapped in insulation, is made of an aluminum section that is 0.20 m Iong and a copper section that is 0.70 m long. Both sections have a cross-sectional area of $0.00040 \mathrm {~m} ^ { 2 }$ The aluminum end and the copper end are maintained at temperatures of $30 ^ { \circ } \mathrm { C } \text { and } 230 ^ { \circ } \mathrm { C }$ respectively. The thermal conductivities of aluminum and copper are 205 W/m . K (aluminum) and $385 \mathrm {~W} / \mathrm { m } \cdot \mathrm { K } \text { (copper). }$ What is the temperature of the aluminum-copper junction in the rod with steady state heat flow?

Heat is added to a 3.0 kg piece of ice at a rate of 636.0 kW. How long will it take for the ice at $0.0 ^ { \circ } \mathrm { C }$ to melt? For water $L F = 334,000 \mathrm {~J} / \mathrm { kg } \text { and } L V = 2.246 \times 10 ^ { 6 } \mathrm {~J} / \mathrm { kg }$

How many grams of ice at $- 17 ^ { \circ } \mathrm { C }$ must be added to 741 grams of water that is initially at a temperature of $70 ^ { \circ } \mathrm { C }$ to produce water at a final temperature of $12 ^ { \circ } \mathrm { C } \text { ? }$ Assume that no heat is lost to the surroundings and that the container has negligible mass. The specific heat of liquid water is $4190 \mathrm {~J} / \mathrm { kg } \cdot \mathrm { C } ^ { \circ }$ and of ice is $2000 \mathrm {~J} / \mathrm { kg } \cdot \mathrm { C } ^ { \circ }$ For water the normal melting point is $0 ^ { \circ } \mathrm { C }$ and the heat of fusion is $334 \times 10 ^ { 3 } \mathrm {~J} / \mathrm { kg }$ The normal boiling point is $100 ^ { \circ } \mathrm { C }$ and the heat of vaporization is $2.256 \times 10 ^ { 6 } \mathrm {~J} / \mathrm { kg }$

A 2294-kg sample of water at $0 ^ { \circ } \mathrm { C }$ is cooled to $- 36 ^ { \circ } \mathrm { C }$ and freezes in the process. How much heat is liberated? For water $L F = 334,000 \mathrm {~J} / \mathrm { kg } \text { and } L V = 2.256 \times 10^6 \mathrm {~J} / \mathrm { kg }$ The specific heat of ice is 2050 $\mathrm { J } / \mathrm { kg } \cdot \mathrm { K }$

A 45.0-kg sample of ice is at $0.00 ^ { \circ } \mathrm { C }$ How much heat is needed to melt it? For water $L F = 334,000$ $\mathrm { J } / \mathrm { kg } \text { and } L V = 2.256 \times 10 ^ { 6 } \mathrm {~J} / \mathrm { kg } \text {. }$