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

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 $\frac{Q}{t}=\frac{kA dT}{dx}$

$\frac{Q}{t}=\frac{0.9\times 0.25\times dT}{0.02}$

$\frac{Q}{t}=11.25dT$----1

Also heat transferred by water

$dQ=-\frac{mc\Delta T}{2}$----2

equating 1 & 2

$-\frac{mc\Delta T}{2}=11.25dT$

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

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