A research laboratory is busy testing a new, rugged, safety switch designed to send out a signal

when the temperature in a fluidised bed exceeds a preset value. The switch system consists of a

hollow metal cylinder of internal volume $400mL$ with a flexible metal diaphragm at one end. When

the pressure in the cylinder exceeds a predetermined value of $6\mathrm{.}25$MPa the metal flexes, forms a

connection between $2$ contacts and an alarm signal sound. By changing the amount and kind of gas

present in the cylinder the temperature at which the alarm sounds can be varied over a wide range.

a$)$ If the alarm is to be set to go off at $640C,$ how many moles of carbon dioxide should be

introduced into the hollow cylinder?

b$)$ If the carbon dioxide were introduced at room temperature $(25C),$ what would the pressure

$($in kPa $)$ of the carbon dioxide in the cylinder be at that temperature? Use the moles calculated

in $(a).$

c$)$ If by mistake, the cylinder was to be filled at $25C$ to the same pressure as that calculated in

$($b$),$ but with carbon monoxide instead of carbon dioxide, at what temperature would the alarm

then sound?

$($Notes: please do not assume ideal gas behaviour of the gas. Provide all references for all data

used in the calculation and attach any related figure to support the calculation$)$

$(7$ marks$)$