250 g of water and equal volume of alcohol of mass 200 g are replaced successively in the same colorimeter and cool from `606^@C` to `55^@C` in 130 s and 67 s, respectively. If the water equivalent of the calorimeter is 10 g, then the specific heat of alcohol in `cal//g^@C` is

Options

A. 1.3
B. 0.67
C. 0.62
D. 0.985

Answer

C

Explanation

Mass of water `=250g`
Mass of alcohol`=200g`
Water equivalent of calorimeter,`W=10g`
Fall of temperature`=60-55=5^@C`
Time taken by water to cool`=130s`
Time taken by alcohol to cool`=67s`
Heat lost by water and colorimeter
`=(250+10)5=260xx5=1300cal`
Rate of loss of heat`=(1300)/(130)=10 cal//s`
Heat lost by alcohol and calorimeter`=(200s+10)5`
Rate of loss of heat `=((200s+10)5)/(67) cal//s`
Heat lost by alcohol and calorimeter`=(200s+10)5`
Rate of loss of heat`=((200s+10)5)/(67) cal//s`
Rates of loss of heat in the two cases are equal
`((200s+10)s)/(67)=10` or `s=0.62 cal//g^@C`