Answer to Question #106211 in Physics for Mesha

Question

A sample of oxygen has an initial temperature, pressure and volume of 25 degrees Celsius,1.00 atm and 2.00 Liters. What is the final temperature if the pressure is increased to 3.50 atm and the volume is decreased to 1.00 Liter?

Answer 1

Using equation of states for an ideal gas, we get

$$\frac{P_1 V_1}{T_1}=\frac{P_2 V_2}{T_2}.$$

Hence

$$T_2=T_1 \frac{P_2}{P_1}\frac{V_2}{V_1}$$ $$T_2=298\:\rm K\times \frac{3.50\:\rm atm}{1.00\:\rm atm}\times \frac{1.00\:\rm L}{2.00\:\rm L}$$

$$=522\:\rm K=249^{\circ}C.$$