A canister containing air has a volume of #85# #cm^3# and a pressure of #1.45# #atm# when the temperature is #310# #K#. What is the pressure when the volume is increased to #180# #cm^3# and the temperature is reduced to #280# #K#?

1 Answer
Mar 2, 2017

Answer:

The pressure will fall to #p_2~~0.523# #atm#

Explanation:

According to the ideal gas equation we know that:

#(pV)/T=const#

so if we write that:

#p_1=1atm#

#v_1=85cm^3#

#T_1=310K#

After the change we have:

#v_2=180cm^3#

#T_2=280K#

We have to calculate the new pressure #p_2#

Using the equation stated at the beginning we have:

#(p_1*v_1)/T_1=(p_2*v_2)/T_2#

If we transform the formula we get:

#p_2=(p_1*v_1*T_2)/(T_1*v_2)#

If we substitute the given data we get:

#p_2=(1*85*310)/(180*280)=2635/5040~~0.523#