The gas in an aerosol container exerts a pressire of 125kPa. The container is thrown on a fire, and this ?

Question

temperature rises to 700 degrees C. What is the pressure at this temperature?

Answer 1

i am presuming that the volume of the gas stays the same, meaning the container does not rupture or explode due to the greater internal pressure

the way to solve for this is to realize that pressure, volume and temperature are related by the perfect gas law...

PV=nRT

if V is constant, and n (the number of moles of gas and thus the amount of gas) are the same, then this equation becomes:

P= kT...meaning the pressure is proportional to the temperature...in other words, double the temperature and you double the pressure

now, we have to be careful to use absolute temperatures when comparing temps...if the gas is originally at room temperature, this equates to an absolute temp of approx 293K (room temp is about 20C and 0C is  273K)

a temp of 700C is equivalent to an absolute temp of 973K

this means that the temp has increased by a factor of 973/293

or by a factor of 3.32

if the temp is now 3.32 times greater, then so is the pressure, so the pressure is now 3.32x125kPa = 415kPa