Exam 14: Heat

Object 1 has three times the specific heat capacity and four times the mass of Object 2. The two objects are given the same amount of heat. If the temperature of Object 1 changes by an amount $\Delta T$ the change in temperature of Object 2 will be

The figure shows a graph of the temperature of a pure substance as a function of time as heat is added to it at a constant rate in a closed container. If $L F$ is the latent heat of fusion of this substance and $L V$ is its latent heat of vaporization, what is the value of the ratio $L V / L F ?$

A 600-g piece of iron at $100 ^ { \circ } \mathrm { C }$ is dropped into a calorimeter of negligible heat capacity containing 100 g of ice at $0 ^ { \circ } \mathrm { C }$ and 120 g of water, also at $0 ^ { \circ } \mathrm { C }$ What is the final temperature of the system? The specific heat of iron is $448 \mathrm {~J} / \mathrm { kg } \cdot \mathrm { K }$ the latent heat of fusion of water is $33.5 \times 10 ^ { 4 } \mathrm {~J} / \mathrm { kg }$ and the specific heat of water is $4186 \mathrm {~J} / \mathrm { kq } \cdot \mathrm { K }$

A blacksmith is flattening a steel plate having dimensions $10 \mathrm {~cm} \times 15 \mathrm {~cm} \times 1 \mathrm {~mm}$ He has heated the plate to 900 K. If the emissivity of the plate is 0.75 , at what rate does it lose energy by radiation? Ignore any heat exchange with the surroundings. $\left( \sigma = 5.67 \times 10 ^ { - 8 } \mathrm {~W} / \mathrm { m } ^ { 2 } \cdot \mathrm { K } ^ { 4 } \right)$

A lab assistant pours 330 g of water at $45 ^ { \circ } \mathrm { C }$ into an 855-g aluminum container that is at an initial temperature of $10 ^ { \circ } \mathrm { C }$ The specific heat of aluminum is $900 \mathrm {~J} / \mathrm { kg } \cdot \mathrm { K }$ and that of water is $4186 \mathrm {~J} / \mathrm { kg } \cdot \mathrm { K }$ What is the final temperature of the system, assuming no heat is exchanged with the surroundings?

A person is walking outdoors on a cold day when the temperature is $- 20 ^ { \circ } \mathrm { C }$ He is breathing at the rate of 16 breaths per minute, and each time he breathes in he inhales $0.0050 m ^ { 3 }$ of air. At what rate does he lose heat from breathing if the air in his lungs is heated to body temperature $\left( 37 ^ { \circ } \mathrm { C } \right)$ before it is exhaled? The specific heat of air is $1020 \mathrm {~J} / \mathrm { kg } \cdot \mathrm { K }$ and the density of air is $1.29 \mathrm {~kg} / \mathrm { m } ^ { 3 }$

A metal has a latent heat of fusion of $2.32 \times 10 ^ { 4 } \mathrm {~J} / \mathrm { kg } _ { 1 }$ a specific heat of $128 \mathrm {~J} / \mathrm { kg } \cdot \mathrm { K } _ { \mathrm { r } }$ and a melting point of $228 ^ { \circ } \mathrm { C } \text {. }$ A 30-g pellet of this metal at $16 ^ { \circ } \mathrm { C }$ hits a solid wall and comes to a complete stop. What would the speed of the pellet have to be in order for it to melt completely when it hits the wall, assuming that all of its kinetic energy is transformed into heat within the pellet?

In grinding a steel knife, the metal can get as hot as $400 ^ { \circ } \mathrm { C }$ If the blade has a mass of 80 g, what is the minimum amount of water needed at $20 ^ { \circ } \mathrm { C }$ if the water is to remain liquid and not rise above $100 ^ { \circ } \mathrm { C }$ when the hot blade is quenched in it? The specific heat of the steel is $0.11 \mathrm { cal } / \mathrm { g } \cdot \mathrm { C } ^ { \circ }$ and the specific heat of water is $1.0 \mathrm { cal } / \mathrm { g } \cdot \mathrm { C } ^ { \circ }$