Water of volume 2 L in a closed container is heated with a coil of 1 kW. While water is heated, the container loses energy at a rate of 160 J/s. In how much time will the temperature of water rise from 27°C to 77°C? (Specific heat of water is 4.2 kJ/kg and that of the container is negligible).

We are given that the volume of water is 2 liters. Since the density of water is 1 kg/L, the mass of water is 2 kg.

The heating coil provides energy at a rate of 1 kW. Since 1 kW equals 1000 W and 1 W is 1 J/s, the coil supplies 1000 J/s.

The container loses energy at a rate of 160 J/s. Therefore, the net energy absorbed by the water per second is the energy supplied by the coil minus the energy lost by the container:

$$ \text{Net energy per second} = 1000 \text{J/s} - 160 \text{J/s} = 840 \text{J/s} $$

The temperature needs to rise from 27°C to 77°C. The change in temperature is:

$$ \Delta T = 77^\circ \text{C} - 27^\circ \text{C} = 50^\circ \text{C} $$

The specific heat of water is given as 4.2 kJ/kg·°C. Converting to joules: 4.2 kJ/kg·°C = 4.2 × 1000 = 4200 J/kg·°C.

The total heat energy required to raise the temperature of the water is given by:

$$ Q = m \cdot c \cdot \Delta T $$

Substituting the values:

$$ Q = 2 \text{kg} \times 4200 \text{J/kg·°C} \times 50^\circ \text{C} $$

First, multiply the mass and specific heat:

$$ 2 \times 4200 = 8400 $$

Then multiply by the temperature change:

$$ 8400 \times 50 = 420000 \text{J} $$

So, the total heat required is 420,000 J.

The net energy supplied per second is 840 J/s. The time $$ t $$ in seconds required to supply 420,000 J is:

$$ t = \frac{\text{Total heat}}{\text{Net energy per second}} = \frac{420000}{840} $$

Simplifying the fraction:

$$ \frac{420000}{840} = \frac{420000 \div 120}{840 \div 120} = \frac{3500}{7} = 500 \text{seconds} $$

Alternatively, note that 840 × 500 = 420,000, so $$ t = 500 $$ seconds.

Converting 500 seconds to minutes and seconds: since 1 minute = 60 seconds,

$$ \text{Minutes} = \left\lfloor \frac{500}{60} \right\rfloor = \left\lfloor 8.333\ldots \right\rfloor = 8 \text{minutes} $$

The remaining seconds are:

$$ 500 - (8 \times 60) = 500 - 480 = 20 \text{seconds} $$

Thus, the time is 8 minutes and 20 seconds.

Comparing with the options, Option A is 8 min 20 s.

Hence, the correct answer is Option A.