In Joly's differential steam calorimeter, 3 g of an ideal gas is contained in a rigid closed sphere at 20°C. The sphere is heated by steam at 100°C and it is found that an extra 0.095 g of steam has condensed into water as the temperature of the gas becomes constant. Calculate the specific heat capacity of the gas in J g^{−1} K^{−1}. The latent heat of vaporisation of water = 540 cal g^{−1 }

#### Solution

For Joly's differential steam calorimeter,

`"C"_"v" = ("m"_2"L")/"m"_1 (theta _ 2 - theta_1),`

where

m_{2} = mass of steam condensed

m_{2} = 0.095 g

Latent heat of vapourization, L = 540 cal/g = 540 × 4.2 J/g

m_{1} = mass of gas present

m_{1} = 3 g

Initial temperature, θ_{1} = 20°C

Final temperature, θ_{2} = 100°C

`=> "C"_"v" = (0.095 xx 540 xx 4.2)/(3 xx (100-20)`

= 0.89 = 0.9 J/ g-K