A glass is cleaned in hot water at 45C and placed on the tab

A glass is cleaned in hot water at 45C and placed on the table bottom up. The room air at 20C that was trapped in the glass is heated up to 40C and some of it leaks out, so the net resulting pressure inside is 2 kPa above the ambient pressure of 101 kPa. Now the glass and the air inside cool down to room temperature. What is the pressure inside the glass?

Solution

For the air inside the glass,

Given P1 = 101 kPa = 101 x10 ³ Pa

         T 1 = 40 ^o C = 40 + 273 = 313 K

         T2 = 20 ^o C = 20 + 273 = 293 K

In this ,volume remains constant.

i.e., V1=V2

Here mass is also constant .i.e., m1 = m2

Or number of moles is constant i.e., n1 = n2

So.from ideal gas equation,P1V1 =nRT1       --------( 1)

      and P2V2 = nRT2    --------( 2)

Equation(2) / equation(1) ==>

P2V2 /P1V1 = nRT2/nRT1

P2/P1 = T2/T1

       P2 = P1 T2 /T 1

            = (103 kPa) (293)/313

            = 96.41 kPa

So, Pressure inside the glass P2 = P1(T1/