The mass, specific heat capacity and the temperature of a solid are `1000g,(1)/(2) cal/g - .^(@)C` and `80^(@)C` respectively. The mass of the liquid and the calorimeter are `900g` and `200g`. Initially,both are at room temperature `20^(@)C` Both calorimeter and the solid are made of same material. In the steady state, temperature of mixture is `40^(@)C`, then specific heat capacity of the unknown liquid.

Answer

A, C

Explanation

`m_1`=mass of solid =`1000g,S_1=`Specific heat of solid`=1/2 cal//g-.^(@)C`
`=S_2` or specific heat of calorimeter
`m_2` = mass of calorimeter `=200g`
`m_3` =mass of unknown liquid `= 900g`
`S_3` =specific heat of unknown liquid
from law of heat exchange,
Heat given by solid= Heat taken by calorimeter + Heat taken by unknown liquid
`:. m_(1)S_(1)|Delta theta_(1)|=m_(2)S_(2)|Delta theta_(2)|+m_(3)S_(3)|Delta theta_(3)|`
`:. 1000xx (1)/(2)xx (80-40)=200xx1/2(40-20)+ 900 xxS_(3)(40-20)`
Solving this equation we get, `S_3=1 cal//g-.^(@) C`.