Water of mass `m = 20 g` is enclosed in a thermally insulated cylinder at the temperature of `0 ^@C` under a weightless piston whose area is `S = 410 cm^2`. The outside pressure is equal to standard atmospheric pressure. To what height will the piston rise when the water absorbs `Q = 20.0 k J` of heat ?

Explanation

Some of the heat used in heating water to the boiling temperature
`T = 100^@C = 373 K`. The remaining heat
=`Q - m c Delta T`
(`c` = specific heat of water, `Delta T = 100 K`) is used to create vapour. If the piston rises to a height `h` then the volume of vapour will be `~~ sh` (neglecting water). Its mass will be `(p_0 sh)/(RT) xx M` and heat of vapourization will be `(p_0 sh Mq)/(RT)`. To this must be added the work done in creating the saturated vapour `~~ p_0 sh`. Thus
`Q - mc Delta T ~~ p_0 S h(1 +(q M)/(RT))` or `h = (Q - mc Delta T)/(p_0 s(1 + (qM)/(RT))) = 20 cm`.