Q4. Which of these are state variables: pressure, volume, temperature, internal energy, heat supplied, work done?
Pressure, volume, temperature and internal energy are state variables. Heat supplied and work done are not: they depend on the path taken between two states.
Q5. A 10 g bullet moving at 400 m s stops in a wooden block fixed to the ground. How much energy becomes internal energy of the bullet and the block, if no energy escapes to the environment and none remains as macroscopic motion or recoverable deformation?
Its kinetic energy, ½ × 0.010 × 400 = 800 J, becomes internal energy of the bullet and the wood. No heat is supplied; the bullet does work on the wood through friction.
Q6. A gas is taken through a series of changes and brought back exactly to its starting pressure, volume and temperature. What is the change in its internal energy?
Zero. Internal energy is a state variable, and the gas is back in its starting state, provided its amount and composition also return to their starting values, whatever heat and work were exchanged along the way.