Question

6 ml of an ideal gas is at a temperature of 250 K. What temperature is required to produce a volume of 9 ml at constant pressure ?

Answer 1

The temperature required to produce a volume of 9 ml is 375 K.

The gas equation can be written:

`(P_1V_1)/(T_1)=(P_2V_2)/T_2`

Where:

`P_1` = the initial pressure
`V_1` = the initial volume
`T_2` = the initial absolute temperature

`P_2` = the final pressure
`V_2` = the final volume
`T_2` = the final absolute temperature

Since we are working at constant pressure `P_1=P_2` so the equation simplifies to :

`(V_1)/(T_1)=(V_2)/(T_2`

Write down the initial conditions:

`V_1`= 6ml
`T_1` = 250K

Then write the final conditions:

`V_2` = 9ml
`T_2` is unknown.

Put in the values:

`(6)/(250)=(9)/(T_2)`

So `T_2`= (9 x 250)/6 = 375 K

Now do a little thought experiment to see if the answer seems sensible. We have raised the temperature and the gas has expanded. Does this sound ok?
Yes it does!