The total distance between the lower fixed point and the upper fiixed point of a thermometer is 12 cm. when this thermometer is palced in a vessel containing 500g water the reading on the scale was 3 cm.. When 10 lead shots at `100^(@)C` were dropped into this container the mercury level int he thermometer rose to 31 mm. find the average heat capacity o the lead shots. (you may leave the answer as a fraction).
Specific heat capacity of water =4.2 kJ `kg^(-1)" "K^(-1)`

Explanation

12 cm`=100^(@)C`
3cm`=x^(@)C`
31mm`=y^(@)C`
Find x and y.
Rise in temperature of water=1nm=`(y-x)K`
Heat gained/lost, `Q=mxxsxxDeltatheta`
Heat capacity `H=mxxs`
`therefore` Heat lsot by theh hot body `=HxxDeltatheta_("lead shots")`
`=H(100-y)`
Calculate the heat gained by the cold water. let this be Q.
Find, `H=(Q)/(100-y)`
If N is the numbe of leads shots.
Average heat capacity `=(Q)/(N(100-y))`