# Worksheet: The First Law of Thermodynamics

In this worksheet, we will practice calculating the change in the internal energy of a system by comparing the heating of and work done by the system.

**Q1: **

A rope is pulled, increasing its tension. The work done pulling the rope is 23 J. While being pulled, the rope is also heated by the hand of the person pulling on it, by a net 1.5 J. What is the change in the ropeβs internal energy? Give your answer to three significant figures.

**Q2: **

A cylinder contains a gas that receives net heating of 15 J. While the gas is heated, the lid of the cylinder is moved upward through a distance of 15 cm, as shown in the diagram. The mass of the lid is 1.45 kg. How much does the internal energy of the gas increase during the heating? Answer to two significant figures.

**Q3: **

A spring is compressed, increasing its tension. The work done compressing the spring is 1.32 J. While being compressed, the spring heats the hand of the person pushing on it by a net of 0.15 J. What is the change in the springβs internal energy? Answer to three significant figures.

**Q4: **

Some liquid in a sealed container receives a net heating, , of 125 J from its surroundings, causing it to expand slightly, as shown in the diagram. The liquid expands more than the container does, and the greater expansion of the liquid exerts a pressure on the container, which deforms it. The elastic potential energy increase due to the containerβs deformation is 15 J. What is the change in the internal energy of the liquid?

**Q5: **

Which of the following formulas correctly represents the change in internal energy of a system, where is the net heating of the system and is the net work done by the system?

- A
- B
- C
- D
- E

**Q6: **

An electric drill has an average useful output power of 55 W during 0.45 s of operation. The power output of the drill is transferred to a brick that has a specific heat capacity of 850 J/kgβ K and a mass of 1.5 kg. The drill and the brick are initially at the same temperature. Because of friction, the brick increases in temperature by 0.012 K while in contact with the drill bit. What is the net useful work done on the brick by the drill if the drill bit is heated by 0.25 J? Answer to three significant figures.

**Q7: **

A bullet loses 375 J of kinetic energy after it
is fired
vertically downward into the sea and travels through
12.5 m of water that has
a density of 1,020 kg/m^{3}.
The path of the bullet through the water
can be modeled as a cylinder of radius 1.5 mm.
This volume of water increases in
temperature by and has a
specific heat capacity of 4,184 J/kgβ
K.
Find the average force exerted on the water by the bullet to
displace it from the bulletβs path. Answer to three significant figures.

- A 31.7 N
- B 20.4 N
- C 22.5 N
- D 37.5 N
- E 14.9 N

**Q8: **

A block of ice at a temperature of is crushed by a 5.2 kg mass piston being dropped a distance of 0.35 m onto the ice. This act is repeated 2,500 times. The piston is initially at a temperature of , is at a final temperature of , and has a specific heat capacity of 550 J/kgβ K. Determine how much ice is melted. Assume none of the work done by the ice on the piston heats it. Use a value of 336 kJ/kg for the specific latent heat of fusion of ice. Answer in grams to three significant figures.

**Q9: **

Water that is initially moving at negligible speed falls over the edge of a 64 m high waterfall and collects in a pool below. The temperature in the pool is uniformly greater than that of the water before it falls. Find the work done on the pool per kilogram of water that passes over the falls. Use a value of 4,184 J/kgβ K for the specific heat capacity of the water. Answer to three significant figures.

- A 523 J/kg
- B 105 J/kg
- C 298 J/kg
- D 627 J/kg
- E 732 J/kg