A geyser heats water flowing at the rate of 3.0 litres per minute from 27 °C to 77 °C. If the geyser operates on a gas burner, what is the rate of consumption of the fuel if its heat of combustion is 4.0 × 10⁴J/g ?

Question

Match List-I with List-II.

List-I	List-II
(A) Heat capacity of body	(I) \( J\,kg^{-1} \)
(B) Specific heat capacity of body	(II) \( J\,K^{-1} \)
(C) Latent heat	(III) \( J\,kg^{-1}K^{-1} \)
(D) Thermal conductivity	(IV) \( J\,m^{-1}K^{-1}s^{-1} \)

Answer 1

Given:

Rate of water flow = 3.0 litres per minute
Density of water ≈ 1 kg per litre
Mass of water heated per minute = 3.0 kg min⁻¹

Initial temperature of water, T₁ = 27 °C
Final temperature of water, T₂ = 77 °C
Rise in temperature, ΔT = 50 K

Specific heat capacity of water, c = 4200 J kg⁻¹ K⁻¹
Heat of combustion of fuel = 4.0 × 10⁴ J g⁻¹

Step 1: Calculate heat required per minute

Heat supplied per minute:

Q = m c ΔT

Q = 3.0 × 4200 × 50

Q = 6.3 × 10⁵ J per minute

Step 2: Calculate heat required per second (power)

Heat supplied per second:

Q̇ = (6.3 × 10⁵) / 60

Q̇ = 1.05 × 10⁴ J s⁻¹

Step 3: Calculate rate of fuel consumption

Let the rate of fuel consumption be ṁ (g s⁻¹)

ṁ × (4.0 × 10⁴) = 1.05 × 10⁴

ṁ = (1.05 × 10⁴) / (4.0 × 10⁴)

ṁ = 0.2625 g s⁻¹

Final Answer:

The rate of consumption of fuel is
0.26 g s⁻¹
(or approximately 15.8 g per minute)

Solution and Explanation