Express the change in internal energy of a system in the following cases:

(i) No heat is absorbed by the system from the surroundings, but work (w) is done on the system. What type of wall does the system have?

(ii) No work is done on the system, but an amount of heat (q) is taken out from the system and given to the surroundings. What type of wall does the system have?

(iii) An amount of work (w) is done by the system, and an amount of heat (q) is supplied to the system. What type of system would it be?

(i) When no heat is absorbed by the system from the surroundings, but work (w) is done on the system, the change in internal energy (ΔU) of the system can be expressed using the first law of thermodynamics:

ΔU = q - w

In this case, q = 0 because no heat is absorbed by the system, and w is negative because work is done on the system. Therefore, the change in internal energy ΔU is negative:

ΔU = 0 - (-w) = w

So, ΔU = w, and the type of wall the system has is an adiabatic wall. An adiabatic wall is a wall that does not allow the transfer of heat between the system and the surroundings.

(ii) When no work is done on the system, but q amount of heat is taken out from the system and given to the surroundings, the change in internal energy (ΔU) of the system can be expressed as:

ΔU = q - w

In this case, w = 0 because no work is done on the system, and q is negative because heat is taken out from the system. Therefore, the change in internal energy ΔU is negative:

ΔU = q - 0 = -q

So, ΔU = -q, and the type of wall the system has is a diathermic wall. A diathermic wall is a wall that allows the transfer of heat between the system and the surroundings.

(iii) When w amount of work is done by the system and q amount of heat is supplied to the system, the change in internal energy (ΔU) of the system can be expressed as:

ΔU = q - w

In this case, both q and w are positive because heat is supplied to the system, and work is done by the system. Therefore, the change in internal energy ΔU is positive:

ΔU = q - w

So, ΔU is positive, and the type of system would be an open system or a system with a conducting wall. An open system allows both heat transfer and work interaction with the surroundings, and a conducting wall allows the transfer of heat between the system and the surroundings.