How do I find the temperature of the air mass, and how do I use a t-skew chart?

Question

So the first problem I'm stuck on is this one:

1. An airmass is moving down a mountain from point A to B. At A the temperature is -10 Celsius and the pressure is 890hPa. At point B the pressure is 1010 hPa. What is the temperature to the air when reaching point B (assuming the airmass is isolated)?

So I thought about using the ideal gas law and $P_1/P_2=T_1/T_2$, but I'm not sure if that is correct. The numbers I get don't look right.

2. The pilot on an airplane thinks it's time to get some fresh air in the cabin. The airpressure outside is 350 hPa and the temperature is -40 Celsius, and the pressure needs to be increased to 850 hPa before being brought into the cabin. This is an adiabatic process. After being compressed what is the temperature of the air?

My teacher says that we need to use the following t-skew diagram.

But I don't understand how to use it in the problem, and which of the lines that represent an adiabatic process.

Answer 1

I don't want to answer your question explicitly because it will ruin your education. Instead, I will guide you by asking three questions:

1. Where on the Skew-T are you?
2. Where on the Skew-T do you want to go?
3. What type of process do you want to undergo to get there? If it is dry and adiabatic, follow the dry adiabat ($\theta=T\left(\frac{P_0}{P}\right)^{\frac{R_d}{c_p}}$)

I recommend drawing the process out. Does the result make sense?