Question #eda19

1 Answer
Feb 19, 2016


T = 109 °C


If the cylinder is sealed (which it appears that it is from the question) then it is not necessary to know the number of moles of gas in the cylinder.

We can use the pressure law to solve the problem, which is:
Pressure is directly proportional to temperature for a fixed mass of gas at constant volume.  In this scenario the volume and mass of gas are constant if we assume that the cylinder does not expand or contract, that no gas escapes and we know that no gas enters.

#p prop T => p_1/T_1= p_2/T_2#
NB temperature just be absolute (i.e. in kelvin).  Also because both pressures are given to us in the same non-SI unit we don't need to convert them to SI units (because the conversion factor would cancel out).

Subscript 1 denotes the initial conditions and 2 denotes the conditions at max pressure.  p₂ is the maximum pressure that the cylinder can take and T₂ is the corresponding temperature.

Rearrange for the unknown which is the final temperature:
#T_2 = p_2/p_1 × T_1#

Convert initial temperature into kelvin:
#T_1 = 20.0 + 273 = 293 K#

Substitute values into the rearranged equation:
#T_2 = 300/230 × 293 = 382.2 K#

Convert the maximum temperature into °C:
#T_2 = 343.0 - 273 = 109.2 °C#