Assignment:
Question 1. Convert Kelvin temperature 2000 K to Celsius.
Question 2. At 32?C, an aluminum ring has an inner diameter of 6 cm and a brass rod has a diameter of 6.01 cm.
If the temperature coefficient of expansion for brass is αb = 1.9 × 10-5 ( ?C)-1 and the temperature coefficient of expansion for aluminum is αa = 2.4 × 10-5 (?C)-1 , to what temperature must the ring be heated so that it will just slip over the rod?
Question 3. To what temperature must both be heated so that the ring just slips over the rod?
Question 4. A 27 gallon steel container is completely filled with carbon tetrachloride. Its temperature is 7 ?C. The average volume coeffi- cient of expansion for carbon tetrachloride is 0.000581(?C)-1 .
How much carbon tetrachloride will spill over when the temperature rises to 26?C? Assume that the steel container is held at constant temperature so that its volume remains constant.
Question 5. A square hole 10.5 cm along each side is cut in a sheet of copper.
Calculate the change in the area of this hole if the temperature of the sheet is increased by 26 K. The coefficient of linear expansion of copper is 1.7 × 10-5 ( ?C)-1.
Question 6. A pendulum clock with a brass suspension system is calibrated so that its period is 1 s at 8 ?C. If the temperature increases to 44 ?C, by how much does the period change?
Question 7. How much time does the clock gain or lose in one week?
Question 8. A car has a 31 L steel gas tank filled to the top with gasoline when the temperature is 8 ?C. Assume the linear expansion coefficient for steel is 1.1 × 10-5 K -1 and the volume expansion of gasoline is 0.0009 K-1 .
Taking the expansion of the steel tank into account, how much gasoline spills out of the tank when the car is parked in the sun and its temperature rises to 45?C?
Question 9. An air bubble originating from an underwater diver has a radius of 6 mm at some depth h. When the bubble reaches the surface
of the water, it has a radius of 7.1 mm. The acceleration of gravity is 9.8 m/s 2.
Assuming the temperature of the air in the bubble remains constant, determine the depth of the diver.
Question 10. Determine the absolute pressure at this depth.
Question 11. A cylinder with a movable piston contains gas at a temperature of 34.9?C, a volume of 2 m3 , and an absolute pressure of 20400 Pa.
What will be its final temperature if the gas is compressed to 0.57 m3 and the absolute pressure increases to 86837 Pa?
Question 12. An auditorium is 9 m high, 41 m long, and 20 m wide.
How many molecules of air are needed to fill the auditorium at 32?C and 99.9 kPa pressure?
The gas constant is 8.31 J/K · mol.
Question 13. A 2 kg block of ice at a temperature of 0.0?C and an initial speed of 6.9 m/s slides across a level floor.
If 330000 J are required to melt 1 kg of ice, how much ice melts, assuming that the initial kinetic energy of the ice block is entirely converted to the ice's internal energy?
Question 14. A 755 kg car moving at 24 m/s brakes to a stop. The brakes contain about 14 kg of iron that absorb the energy.
What is increase in temperature of the brakes? Assume the specific heat of iron is 450 J/kg · ? C.
Question 15. A 4.9 g lead bullet moving at 278 m/s strikes a steel plate and stops.
If all its kinetic energy is converted to thermal energy and none leaves the bullet, what is its temperature change? Assume the specific heat of lead is 128 J/kg/ ?C.
Question 16. A 0.013 g cube of ice at 0?C is added to 0.442 g of soup at 81.1 ?C.
The specific heat of water is 4186 J/kg · ?C and the latent heat of fusion for water is 333000 J/kg.
Assuming that the soup has the same specific heat capacity as water, find the final temperature of the soup after the ice has melted.
Question 17. At a foundry, 24 kg of molten aluminum with a temperature of 660.4 ?C is poured into a mold.
The specific heat of aluminum is 899 J/kg · ?C and its latent heat of fusion is 397000 J/kg.
If this is carried out in a room containing 140 kg of air at 25?C, what is the temperature of the air after the aluminum is completely solidified? Assume that the specific heat capacity of air is 1000 J/kg ·?C and that the melting point of aluminum is 660.4?C.