A gas based geyser heats water flowing at the rate of 5.0 litres per minute from 27°C to 87°C.
The rate of consumption of the gas i $s ____$ g·s⁻¹.
(Take heat of combustion of gas = 5.0 × 10⁴ J·g⁻¹) specific heat capacity of water = 4200 J·kg⁻¹·°C⁻¹

Question

A gas based geyser heats water flowing at the rate of 5.0 litres per minute from 27°C to 87°C.

The rate of consumption of the gas i $s ____$ g·s⁻¹.

(Take heat of combustion of gas = 5.0 × 10⁴ J·g⁻¹) specific heat capacity of water = 4200 J·kg⁻¹·°C⁻¹

G1 Physics · Accepted Answer

Water flow rate is 5 /60 kg·s⁻¹. The temperature rise is ΔT = 87-27 = 60°C. The power required to heat the flowing water is P = dm /dt cΔT = 5 / 60 × 4200 × 60 = 21000 W. Let the gas-consumption rate be x g·s⁻¹. The energy supplied by the gas per second is P = x × 5.0 × 10⁴. Hence, x × 5.0 × 10⁴ = 21000. Therefore, x = 0.42 g·s⁻¹. Correct option: C.

A gas based geyser heats water flowing at the rate of 5.0 litres per minute from 27°C to 87°C. The rate of consumption of the gas i s ____ g·s⁻¹. (Take heat of combustion of gas = 5.0 × 10⁴ J·g⁻¹) specific heat capacity of water = 4200 J·kg⁻¹·°C⁻¹