Exam 14: Heat

An 920-g piece of iron at $100 ^ { \circ } \mathrm { C }$ is dropped into a calorimeter of negligible heat capacity containing 50 g of ice at $0 ^ { \circ } \mathrm { C }$ and 92 g of water, also at $0 ^ { \circ } \mathrm { C }$ What is the final temperature of the system? The specific heat of iron is 448 $\mathrm { J } / \mathrm { kg } \cdot \mathrm { K }$ that of water is 4186 $\mathrm { J } / \mathrm { kg } \cdot \mathrm { K } _ { 1 }$ , and the latent heat of fusion of water is $33.5 \times 10 ^ { 4 } \mathrm {~J} / \mathrm { kg }$

A .20-kg ice cube at $0.0 ^ { \circ } \mathrm { C }$ has sufficient heat added to it to cause total melting, and the resulting water is heated to $70.0 ^ { \circ } \mathrm { C }$ How much heat is added? For water $L _ { F } = 334,000 \mathrm {~J} / \mathrm { kg } , L \mathrm {~V} = 2.256 \times 10 ^ { 6 }$ $\mathrm { J } / \mathrm { kq } _ { \text {, the } c } = 4.186 \times 10 ^ { 3 } \mathrm {~J} / \mathrm { kq } \cdot \mathrm { C } \text {. }$

A person makes iced tea by adding ice to 1.8 kg of hot tea, initially at $80 ^ { \circ } \mathrm { C }$ How many kilograms of ice, initially at $0 ^ { \circ } \mathrm { C }$ are required to bring the mixture to $10 ^ { \circ } \mathrm { C } ?$ The specific heat of water (and tea) is $4186 \mathrm {~J} / \mathrm { kg } \cdot \mathrm { K }$ and the latent heat of fusion of ice is $3.34 \times 10 ^ { 5 } \mathrm {~J} / \mathrm { kg }$

A 400-g stainless steel tea kettle containing 500 g of water is on the stove. The portion of the tea kettle that is in contact with the heating element has an area of $0.090 \mathrm {~m} ^ { 2 }$ and is 2.0 mm thick. At a certain moment, the temperature of the water is $75 ^ { \circ } \mathrm { C }$ and it is rising at the rate of $3.0 \mathrm { C } ^ { \circ }$ per minute. What is the difference in temperature between the inside and the outside of the bottom of the tea kettle? Assume that the inner surface of the kettle is at the same temperature as the water inside. The thermal conductivity of stainless steel is $16.3 \mathrm {~W} / \mathrm { m } \cdot \mathrm { K }$ the specific heat of the steel is 448 $\mathrm { J } / \mathrm { Kg } \cdot \mathrm { K }$ and the specific heat of water is 4186 $\text { J/kg. K. }$

On his honeymoon, James Joule attempted to explore the relationships between various forms of energy by measuring the rise of temperature of water which had fallen down a waterfall on Mount Blanc. What maximum temperature rise would one expect for a waterfall with a vertical drop of 20 m? The specific heat of water is $4186 \mathrm {~J} / \mathrm { kg } \cdot \mathrm { K }$

The water flowing over Niagara Falls drops a distance of 50 m. If all the gravitational potential energy is converted to thermal energy, by what temperature does the water rise? The specific heat of water is $4186 \mathrm {~J} / \mathrm { kg } \cdot \mathrm { K }$

A solid concrete wall has dimensions 4.0 m x 2.4 m and is 30 cm thick. The thermal conductivity of the concrete is $1.3 \mathrm {~W} / \mathrm { m } \cdot \mathrm { K }$ and it separates a basement from the ground outside. The inner surface of the wall is at $18 ^ { \circ } \mathrm { C }$ and the outside surface is at $6 ^ { \circ } \mathrm { C }$ How much heat flows through the wall every hour?

A 920-g empty iron kettle is put on a stove. How much heat in joules must it absorb to raise its temperature form $15.0 ^ { \circ } \mathrm { C } \text { to } 93.0 ^ { \circ } \mathrm { C } \text { ? }$ The specific heat for iron is $113 \mathrm { cal } / \mathrm { kg } \cdot \mathrm { C } ^ { \circ }$ and 1 cal=4.186 J

Two metal rods, one silver and the other copper, are both immersed at one end in a steam chamber at a temperature of $100 ^ { \circ } \mathrm { C } \text {. }$ The other end of each one is in an ice water bath at $0 ^ { \circ } \mathrm { C }$ The rods are 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 the 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 copper is 395 $\mathrm { W } / \mathrm { m } \cdot \mathrm { K } .$

It is necessary to determine the specific heat of an unknown object. The mass of the object is 201.0 g. It is determined experimentally that it takes 15.0 J to raise the temperature $10.0 ^ { \circ } \mathrm { C }$ What isthe specific heat of the object?

What is the net power radiated by a little animal with a surface area of $0.075 \mathrm {~m} ^ { 2 }$ if his emissivity is 0.75 , his skin temperature is 315 K, and he is in a room with a temperature of 290 K? $( \sigma = 5.67 \times$ $\left. 10 ^ { - 8 } \mathrm {~W} / \mathrm { m } ^ { 2 } \cdot \mathrm { K } ^ { 4 } \right)$

How much heat must be removed from 456 g of water at $25.0 ^ { \circ } \mathrm { C }$ to change it into ice at $- 10.0 ^ { \circ } \mathrm { C } ?$ The specific heat of ice is $2090 \mathrm {~J} / \mathrm { kg } \cdot \mathrm { K }$ the latent heat of fusion of water is $33.5 \times 10 ^ { 4 } \mathrm {~J} / \mathrm { kg }$ and the specific heat of water is $4186 \mathrm {~J} / \mathrm { kg } \cdot \mathrm { K }$

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 $m ^ { 2 }$ 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 thermal conductivity of alloy A?

A sphere of surface area $1.25 \mathrm {~m} ^ { 2 }$ and emissivity 1.0 is at a temperature of $100 ^ { \circ } \mathrm { C }$ At what rate does it radiate heat into empty space? $\left( \sigma = 5.67 \times 10 ^ { - 8 } \mathrm {~W} / \mathrm { m } ^ { 2 } \cdot \mathrm { K } ^ { 4 } \right)$

The thermal conductivity of a certain concrete is 0.80 $\mathrm { W } / \mathrm { m } , \mathrm { K }$ and the thermal conductivity of a certain wood is 0.10 $\mathrm { W } / \mathrm { m } \cdot \mathrm { K }$ How thick would a solid concrete wall have to be in order to have the same rate of heat flow through it as an 8.0-cm thick wall made of solid wood? Both walls have the same surface area and the same temperature difference across their faces.

Solar houses use a variety of energy storage devices to retain the heat absorbed during the day so that it can be released during the night. Suppose that you were to use a device of this kind to produce steam at $100 ^ { \circ } \mathrm { C }$ during the day, and then allow the steam to cool to $0 ^ { \circ } \mathrm { C }$ and freeze during the night. How many kilograms of water would be needed to store 20.0 kWh of energy in this way? The latent heat of vaporization of water is $22.6 \times 10 ^ { 5 } \mathrm {~J} / \mathrm { kg }$ the latent heat of fusion of water is $33.5 \times 10 ^ { 4 } \mathrm {~J} / \mathrm { kg }$ and the specific heat capacity of water is $4186 \mathrm {~J} / \mathrm { kg } \cdot \mathrm { K }$

In an experiment to measure the thermal conductivity of a certain material, a slab of material 10.0 mm thick separates a steam chamber from a block of ice with a square cross-section with dimensions $8.00 \mathrm {~cm} \times 8.00 \mathrm {~cm}$ After 5.00 min of running the experiment, 64.0 g of ice have melted. What is the thermal conductivity of this material? The latent heat of fusion of water is $33.5 \times 10 ^ { 4 }$ J/Kg, the latent heat of vaporization of water is $2.256 \times 10 ^ { 6 } \mathrm {~J} / \mathrm { kg }$ and both the ice and water are under 1.00 atm of pressure.

A 40.0-g block of ice at - $15.00 ^ { \circ } \mathrm { C }$ is dropped into a calorimeter (of negligible heat capacity) containing water at $15.00 ^ { \circ } \mathrm { C }$ When equilibrium is reached, the final temperature is $8.00 ^ { \circ } \mathrm { C }$ How much water did the calorimeter contain initially? 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 $33.5 \times 10 ^ { 4 } \mathrm {~J} / \mathrm { kg }$

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 it take before the temperature starts to rise above $0 ^ { \circ } \mathrm { C } ?$ The specific heat of ice is $2090 \mathrm {~J} / \mathrm { kg } .$ $\mathrm { K }$ and the latent heat of fusion of water is $33.5 \times 10 ^ { 4 } \mathrm {~J} / \mathrm { kg }$

A glass tea kettle containing 500 g of water is on the stove. The portion of the tea kettle that is in contact with the heating element has an area of $0.090 \mathrm {~m} ^ { 2 }$ and is 1.5 mm thick. At a certain moment, the temperature of the water is $75 ^ { \circ } \mathrm { C }$ and it is rising at the rate of $3 \mathrm { C } ^ { \circ }$ per minute. What is the temperature of the outside surface of the bottom of the tea kettle? Neglect the heat capacity of the kettle, and assume that the inner surface of the kettle is at the same temperature as the water inside. The thermal conductivity of glass is $0.840 \mathrm {~W} / \mathrm { m } \cdot \mathrm { K }$ and the specific heat of water is 4186 $\mathrm { J } / \mathrm { kq } \cdot \mathrm { K }$