In a thermally insulated tube of cross sectional area `4cm^(2)` a liquid of thermal expansion coefficeint `10^(3)K^(-1)` is flowing. Its velocity at the entrance is `0.1m//s`. At the middle of the tube a heater of a power of 10 kW is heating the liquid. The specific heat capacity of the liquid is 1.5 kJ/(kg,K), and its density is `1500kg//m^(3)` at the entrance.
Q. What is the density of liquid at the exit?

Options

A. `1000/9 (^(@)C)`
B. `1/9(^(@)C)`
C. `500/9(^(@)C)`
D. None of these

Answer

A

Explanation

`rho_(1)v_(1)A_(1)=rho_(2)v_(2)A_(2)`
`m=1500kg//m^(3)xx0.1m//sxx4(cm)^(2)`
`msDeltaT=1000`
`1500xx0.1xx4xx10^(-4)xx1500xxDeltaT=10000`
`DeltaT=10000/90=1000/9`