Answer
a) $\Delta t = 17170s=4.77h$
b) $\Delta t = 33333s=9.26h$
Work Step by Step
The mass of 50 containers of 20L each of water $\rho=1kg/L$ is $m=1000\ kg$
a)
The energy balance for the system reduces to:
$Q-W_e=\Delta U_{water}=mc_v(T_2-T_1)$
Given:
$Q=-50000\ kJ/h \times 10 h = -500\ MJ$
$W_e=-15\ kW\times \Delta t(s)$
Given $c_v=4.18\ kJ/kg.K,\ T_2=22°C, T_1=80°C$:
we can solve for the length of time: $\Delta t = 17170s=4.77h$
b)
Without solar heating the energy balance would be:
$Q-W_e=0$
Hence:
$\Delta t = 33333s=9.26h$
