Exam 14: Heat

An aluminum electric tea kettle with a mass of 500 g is heated with a 500 -W heating coil. How Iong will it take to heat up 1.0 kg of water from $18 ^ { \circ } \mathrm { C } \text { to } 98 ^ { \circ } \mathrm { C }$ in the tea kettle? The specific heat of aluminum is 900 $\mathrm { J } / \mathrm { kg } \cdot \mathrm { K }$ and that of water is 4186 $\mathrm { J } / \mathrm { kg } \cdot \mathrm { K } .$

11A 90-g aluminum calorimeter contains 390 g of water at an equilibrium temperature of $20 ^ { \circ } \mathrm { C }$ A 160-g piece of metal, initially at $305 ^ { \circ } \mathrm { C }$ is added to the calorimeter. The final temperature at equilibrium is $32 ^ { \circ } \mathrm { C }$ Assume there is no external heat exchange. The specific heat capacities of aluminum and water are 910 $\mathrm { J } / \mathrm { kg } \cdot \mathrm { K }$ (aluminum) and 4190 $\mathrm { J } / \mathrm { kg } \cdot \mathrm { K }$ (water). What is the specific heat capacity of the 160-\mathrm{g} piece of metal?

How much heat must be added to a 8.0 -kg block of ice at $- 8 ^ { \circ } \mathrm { C }$ to change it to water at $14 ^ { \circ } \mathrm { C } ?$ The specific heat of ice is $2050 \mathrm {~J} / \mathrm { kg } \cdot \mathrm { C } ^ { \circ }$ the specific heat of water is $4186 \mathrm {~J} / \mathrm { kg } \cdot \mathrm { C } ^ { \circ }$ the latent heat of fusion of ice is 334,000 J/kg, and 1cal=4.186 J.

A 400-g block of iron at $400 ^ { \circ } \mathrm { C }$ is dropped into a calorimeter (of negligible heat capacity) containing 60 g of water at $30 ^ { \circ } \mathrm { C }$ How much steam is produced? The latent heat of vaporization of water is $22.6 \times 10 ^ { 5 }$ J/kg and its specific heat capacity is 4186 $\mathrm { J } / \mathrm { Kg } \cdot \mathrm { K }$ The average specific heat of iron over this temperature range is $560 \mathrm {~J} / \mathrm { kg } \cdot \mathrm { K } .$

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 $\mathrm { W } / \mathrm { m } \cdot \mathrm { K }$ (wood). What should be the thickness of the layer of wood?

Object 1 has three times the specific heat capacity and four times the mass of Object 2 . The two objects are heated from the same initial temperature, $T _ { 0 }$ to the same final temperature $T _ { \mathbf { f } }$ During this process, if Object 1 absorbs heat Q , the amount of heat absorbed by Object 2 will be

A heat conducting rod, 1.60 m Iong and wrapped in insulation, is made of an aluminum section that is 0.90 m long 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 $30 ^ { \circ } \mathrm { C } \text { and } 170 ^ { \circ } \mathrm { C }$ Respectively. The thermal conductivities of aluminum and copper are 205 W/m . K (aluminum) and $385 \mathrm {~W} / \mathrm { m } \cdot \mathrm { K } \text { (copper). }$ At what rate is heat conducted in the rod under state conditions?

If you add 700 kJ of heat to 700 g of water originally at $70.0 ^ { \circ } \mathrm { C }$ how much water is left in the container? The latent heat of vaporization of water is $22.6 \times 10 ^ { 5 } \mathrm {~J} / \mathrm { kg }$ and its specific heat capacity is $4186 \mathrm {~J} / \mathrm { kg } \cdot \mathrm { K } .$

When 50 g of a certain material at $100 ^ { \circ } \mathrm { C }$ is mixed with 100 g of water at $0 ^ { \circ } \mathrm { C }$ the final temperature is $40 ^ { \circ } \mathrm { C }$ What is the specific heat of the material? The specific heat of water is $1.00 \mathrm { kcal } / \mathrm { kq } \cdot \mathrm { C } ^ { \circ }$

Two metal rods are to be used to conduct heat from a region at $100 ^ { \circ } \mathrm { C }$ to a region at $0 ^ { \circ } \mathrm { C }$ as shown in the figure. The rods can be placed in parallel, as shown on the left, or in series, as on the right. When steady state flow is established, the heat conducted in the series arrangement is

A 35-g block of ice at - $14 ^ { \circ } \mathrm { C }$ is dropped into a calorimeter (of negligible heat capacity) containing 400 g of water at $0 ^ { \circ } \mathrm { C }$ When the system reaches equilibrium, how much ice is left in the calorimeter? 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 rod, with sides insulated to prevent heat loss, has one end immersed in boiling water at $100 ^ { \circ } \mathrm { C }$ and the other end in a water-ice mixture at $0 ^ { \circ } \mathrm { C }$ The rod has uniform cross-sectional area $7.05 \mathrm {~cm} ^ { 2 }$ and length 87 cm. The heat conducted by the rod melts the ice at a rate of 1.0 g every 11 seconds. What is the thermal conductivity of the rod? Recall that the heat of fusion of water is $3.34 \times 10 ^ { 5 } \mathrm {~J} / \mathrm { kg }$

A person tries to heat up her bath water by adding 5.0 L of water at $80 ^ { \circ } \mathrm { C }$ to 60 L of water at $30 ^ { \circ } \mathrm { C }$ What is the final temperature of the bath water?

Some properties of a certain glass are listed here: Density $2300 \mathrm {~kg} / \mathrm { m } ^ { 3 }$ Specific heat capacity $\quad 840 \mathrm {~J} / \mathrm { kg } \cdot \mathrm { C } ^ { \circ }$ Coefficient of thermal expansion $8.5 \times 10 ^ { - 6 } \left( \mathrm { C } ^ { \circ } \right) ^ { - 1 }$ Thermal conductivity $\quad 0.80 \mathrm {~W} / \mathrm { m } \cdot \mathrm { C } ^ { \circ }$ A glass window pane is 2.7 m high, 2.4 m wide, and 9.0 mm thick. The temperature at the inner surface of the glass is $19 ^ { \circ } \mathrm { C }$ and at the outer surface $4 ^ { \circ } \mathrm { C }$ How much heat is lost each hour through the window?

If 150 kcal of heat raises the temperature of 2.0 kg of a material by 400 F°, what is the specific heat capacity of the material?

A lab assistant drops a 400.0-g piece of metal at $100.0 ^ { \circ } \mathrm { C }$ into a 100.0-g aluminum cup containing 500.0 g of water at $15.0 ^ { \circ } \mathrm { C }$ In a few minutes, she measures the final temperature of the system to be $40.0 ^ { \circ } \mathrm { C }$ What is the specific heat of the 400.0-g piece of metal, assuming that no significant heat is exchanged with the surroundings? The specific heat of this aluminum is $900.0 \mathrm {~J} / \mathrm { kg } \cdot \mathrm { K }$ and that of water is $4186 \mathrm {~J} / \mathrm { kg } \cdot \mathrm { K }$

A runner generates 1260 W of thermal energy. If this heat has to be removed only by evaporation, how much water does this runner lose in 15 minutes of running? The latent heat of vaporization of water is $22.6 \times 10 ^ { 5 } \mathrm {~J} / \mathrm { kg }$

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 $900 \mathrm {~J} / \mathrm { kg } \cdot \mathrm { K }$ How much heat must be added to 500 g of aluminum at $27 ^ { \circ } \mathrm { C }$ to completely melt it?

A substance has a melting point of $20 ^ { \circ } \mathrm { C }$ and a heat of fusion of $3.4 \times 10 ^ { 4 } \mathrm {~J} / \mathrm { kg }$ The boiling point is $150 ^ { \circ } \mathrm { C }$ and the heat of vaporization is $6.8 \times 10 ^ { 4 } \mathrm {~J} / \mathrm { kg }$ 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 $\text { J/kg } \cdot K \text { (gaseous). }$ How much heat is required to raise the temperature of 1.90 kg of this substance from $- 4 ^ { \circ } \mathrm { C } \text { to } 106 ^ { \circ } \mathrm { C }$ at a pressure of one atmosphere?

A camper is about to drink his morning coffee. He pours 400 grams of coffee, initially at $75 ^ { \circ } \mathrm { C }$ into a 250-g aluminum cup, initially at $16 ^ { \circ } \mathrm { C }$ What is the equilibrium temperature of the coffee-cup system, assuming no heat is lost to the surroundings? The specific heat of aluminum is 900 $\mathrm { J } / \mathrm { kg } \cdot \mathrm { K }$ and the specific heat of coffee is essentially the same as that of water, which is $4186 \mathrm {~J} / \mathrm { kg } \cdot \mathrm { K }$