Question

For the following three processes, state whether each of the four thermodynamic quantities q, w, ΔU, and ΔH is greater than, equal to, or less than zero for the system described. Briefly explain your reasoning for each answer.

a. Two copper bars, one initially at 80 °C and the other initially at 20 °C are brought into contact with each other in a thermally insulated compartment and then allowed to come to equilibrium.

b. A sample of liquid in a thermally insulated container (a calorimeter) is stirred for 1 hour by a mechanical linkage to a motor in the surroundings.

c. An ideal gas is compressed in a frictionless piston to half its initial volume at constant pressure.

d. An ideal gas is compressed in a frictionless piston to half its initial volume at constant temperature.

Answer 1

a)

assume the "system" are both bars. Then total energy is conserved since we assume no exchange with the exterior. Since those are solid, the volume chang eis neglebile so

Q = 0; W = 0, dU = dH = 0

b)

q = 0 (no heat added)

dU = increases

W = increases

dH = increases since dU increased

c)

Q = 0 since it is fricitonless

dU increases, since T increases (due to ideal gas law)

dH incresase since dU increased

W = increases in the system, since work was applied to it

d)

Q = 0 since it is fricitonless

dU remains, since T is constant

dH incresase since PV changes, it increased

W = increases in the system, since work was applied to it