Question

A large container is separated into two halves by al= 2.0 cm thick glass divider. The area of the divider is= 0.25 m2and the thermal conductivity of glass isk= 0.90 W/m·K. Each side is filled withm= 30 kg of water, specific heatc= 4180 J/kg·K, at different temperatures. Initially, the temperature difference is ∆T0= 20 K. How long will it take before the temperature difference is ∆T= 1.0 K

Answer 1

Answer:4.6 hr

Step-by-step explanation:

Given

area of divider is 0.25 m^2

conductivity of glass k=0.9 W/m.K

mass of water =30 kg

specific heat c=4180 J/kg.K

initial temperature difference
`T_1=20 K`

Final temperature difference
`T_2=1 K`

Let Temperature difference be T so change in temperature difference is given by dT in time dt

rate of heat flow is
`(Q)/(t)=(kA dT)/(dx)`

`(Q)/(t)=(0.9* 0.25* dT)/(0.02)`

`(Q)/(t)=11.25dT`----1

Also heat transferred by water

`dQ=-(mc\Delta T)/(2)`----2

equating 1 & 2

`-(mc\Delta T)/(2)=11.25dT`

`-62700\frac{\mathrm{d} T}{\mathrm{d} T}=11.25dt`

integrating for T=20 to T=1 for time t

`\left ( -62700\ln T\right )_(20)^1=t`

t=16696.2 s

t=4.6 hr