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 ?

1 Answer
Michael
Oct 15, 2014

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!

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