A question about opening a jam jar

When jam is made, it is put into the jam jar and the top screwed down whilst the jam is still

hot. The top makes an airtight seal with the jar and the air trapped above the jam cools and

so the pressure of the trapped air reduces.

$6cm$

Useful information:

For the air

$\frac{p}{T}=$ constant

assuming no air escapes$/$enters and the volume

of the trapped air remains constant

$p=$ pressure of the trapped air

$T=$ Temperature in Kelvin

Atmospheric pressure $=100$kPa

$($at room temperature$)$

Absolute zero $=-273C$

a$)$ Calculate the force, due to atmospheric pressure, acting downwards on the top of the circular

lid of the jam jar

$[3$ marks$]$

b$)$ The jam and the trapped air were initially at a temperature of $85C$ when the jam was put

into the jar and lid secured.

Show that the pressure of the trapped air, once it has cooled to a room temperature of $15C$

inside the jar is approximately $80$kPa

$[3$ marks$]$