The question asks what happens to the CAS when an aircraft is climbing through an isothermal layer at a constant Mach. You are therefore looking for a CAS / Mach relationship.

 

Mach = Dynamic pressure/Static pressure = CAS/Static Pressure

 

Using this equation you do not need to take account of the temperature, but purely the affect of altitude.

As the aircraft is climbing the static pressure will be decreasing and therefore to maintain a constant Mach the CAS must also decrease, which is the answer to this question.

 

Conversely if the aircraft is descending then the static pressure will increase, so CAS will increase to maintain a constant Mach.

 

If the aircraft remains at a constant flight level then the static pressure will remain constant and the CAS must also remain constant to maintain a constant Mach.

 

Furthermore if the question is related to TAS and Mach use the following formula;

Mach = TAS/LSS where the LSS is solely dependent on temperature.

 

If an aircraft is climbing at a constant Mach through an isothermal layer the temperature will remain constant, so the LSS will remain constant and TAS will remain constant.

 

Conversely if an aircraft is climbing at a constant Mach through an inversion what will happen to TAS. With increasing altitude the LSS will decrease, but because the aircraft is flying through an inversion the temperature will increase, which will cause the LSS to increase and therefore the TAS to increase.