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 of 1.5 J. What is the change in the rope’s internal energy? Give your answer to one decimal place.

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? Give your answer to the nearest joule.

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 spring’s internal energy?

Q4:

Some liquid in a sealed container receives a net heating, Ξ”π‘„βˆ’Ξ”π‘„inout, 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 container’s 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 Δ𝑄 is the net heating of the system and Ξ”π‘Š is the net work done by the system?

  • AΔ𝐸=Ξ”π‘ŠΞ”π‘„
  • BΔ𝐸=Δ𝑄+Ξ”π‘Š
  • CΔ𝐸=Ξ”π‘„Ξ”π‘Š
  • DΔ𝐸=Ξ”π‘„β€“Ξ”π‘Š
  • EΔ𝐸=Ξ”π‘Šβ€“Ξ”π‘„

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? Give your answer to one decimal place.

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/m3. 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 0.25∘C 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 bullet’s path. Give your answer to one decimal place.

Q8:

A block of ice at a temperature of 0∘C 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 has an initial temperature of 20∘C, a final temperature of 18∘C, and 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. Give your answer to the nearest gram.

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 0.025∘C 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. Give your answer to the nearest joule per kilogram.

Q10:

Some ice is crushed by a piston being dropped through a distance onto the ice, as shown in the diagram. The quantities π‘ŠοŠ§ and π‘ŠοŠ¨ represent mechanical work and the quantities π‘„οŠ§ and π‘„οŠ¨ represent heating.

Which of the four quantities represents the heating of the ice by the piston?

  • Aπ‘ŠοŠ§
  • Bπ‘„οŠ¨
  • Cπ‘ŠοŠ¨
  • Dπ‘„οŠ§

Which of the four quantities represents the work done by the ice on the piston?

  • Aπ‘„οŠ§
  • Bπ‘ŠοŠ¨
  • Cπ‘ŠοŠ§
  • Dπ‘„οŠ¨

Which of the four quantities represents the work done by the piston on the ice?

  • Aπ‘ŠοŠ¨
  • Bπ‘ŠοŠ§
  • Cπ‘„οŠ§
  • Dπ‘„οŠ¨

Which of the four quantities represents the heating of the piston by the ice?

  • Aπ‘„οŠ§
  • Bπ‘ŠοŠ¨
  • Cπ‘ŠοŠ§
  • Dπ‘„οŠ¨

What combination of quantities represents the change in the internal energy of the ice?

  • Aπ‘Šβˆ’π‘Š+π‘„βˆ’π‘„οŠ¨οŠ§οŠ¨οŠ§
  • Bπ‘Šβˆ’π‘Š+π‘„βˆ’π‘„οŠ¨οŠ§οŠ§οŠ¨
  • Cπ‘Šβˆ’π‘Š+π‘„βˆ’π‘„οŠ§οŠ¨οŠ§οŠ¨
  • Dπ‘Šβˆ’π‘Š+π‘„βˆ’π‘„οŠ§οŠ¨οŠ¨οŠ§

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