Discussion Forum

1)

A water cooler of storage capacity 120 litres can cool water at a constant rate of P watts. In a closed circulation system (as shown schematically in the figure), the water from the cooler is used to cool an external device that generates constantly 3 kW of heat (thermal load). The temperature of water fed into the device cannot exceed 30⁰C and the entire stored 120 litres of water is initially cooled to 10⁰C . The entire system is thermally insulated. The minimum value of P (in watts) for which the device can be operated for 3 hours is

(Specific heat of water is 4.2kJ kg^-1 K^-1 and the density of water is l000kg m^-3 ) 

 

 

Answer:

Option B

Explanation:

 Heat generated in device in 3 h = Time x power

= $3\times 3600\times 3\times 10^{3}$

$=324\times 10^{5} J$

Heat used to heat water = msΔθ

= $120\times l\times 4.2\times 10^{3}\times 20$

Heat absorbed by coolant

Pt = $324\times 10^{5}-120\times l\times 4.2\times 10^{3}\times 20J$

Pt = $(325-100.8)\times 10^{5} J$

$=223.2\times 10^{5}$

$P=\frac{223.2\times 10^{5}}{3600}$

=2067 W