Gas Laws And Adiabatic Process

Question

Air at 20 degrees Celsius is compressed adiabatically from 1 bar to 10 bar, what will its temperature be?

With $$P_1 = 1,$$ $$P_2 = 10$$ $$T_1 = 293K,$$ $$T_2 = unknown$$ using $$\dfrac{P_1}{P_2}=\dfrac{T_1}{T_2}$$ my solution was $$\dfrac{1}{10}=\dfrac{293}{T_2}$$ giving $$T_2 = 2930$$

My physics tutor said this is wrong and I should use $P_1V_1^\lambda=P_2V_2^\lambda$ and then use $\dfrac{V_1}{V_2}=\dfrac{T_1}{T_2}$ to find the temperature.

The only problem I now have is that $V_1 = V_2 = unknown$ which is making me think that he may have forgot to add that information to the question.

I would like to know if there is anyway to solve this (I do not want the answer just a point in the right direction).

thanks in advance!

Answer 1

*The only problem I now have is that $V1=V2$=unknown which is making me think that he may have forgot to add that information to the question. *

I belive that's the problem. You can't have $V1=V2$ in an adiabatic process (suposing that the number of particles is constant).

Your tutor already pointed the right direction, combine $P_1V_1^\lambda=P_2V_2^\lambda$ with the ideal gas law, and this should be enough to eliminate the $V$ dependence. ($V_1/V_2=T_1/T_2$ already comes from ideal gas law)