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. (Adapted from Tinoco, 2.15)
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)
The system is completed isolated from outside
Hence q = 0 and ΔH

Work is not getting exchanged between outside and inside. this is correct because the two rods came in equilibrium all by themselves
so,
w = 0

Since w = 0 and q = 0
ΔU = 0 as ΔU = q+w

b)
SInce the container is insulated, q = 0
Since container is at constant pressure and ΔH= q at constant pressure,
ΔH = 0

Since container is getting stirred, work is being done on it
So, W > 0

ΔU = q + W
since q =0 and W>0, ΔU>0

c)
W = -P*(delta V) , since delta V is negative,
W > 0

There is no heat transfer occuring
SO, q = 0

ΔU = q + W
so, ΔU > 0

Incraese in ΔU indicates incraese in temperature
So,
ΔH > 0 as ΔH = Cp(T2-T1)

d)
W = -P*(delta V) , since delta V is negative,
W > 0

SInce Temperature is constant,
ΔH and ΔU = 0

ΔU = q + W
since W > 0, q<0 to make ΔU=0
So, q<0