Question:
A geyser heats water flowing at the rate of 3.0 liters per minute from 27°C to 77°C. If the geyser operates on a gas burner and if its heat of combustion is \( 4.0 \times 10^4 \text{ J g}^{-1} \), the rate of combustion of the fuel per minute is:
A geyser heats water flowing at the rate of 3.0 liters per minute from 27°C to 77°C. If the geyser operates on a gas burner and if its heat of combustion is \( 4.0 \times 10^4 \text{ J g}^{-1} \), the rate of combustion of the fuel per minute is:
Show Hint
When calculating fuel consumption, ensure consistent units for energy (Joules) and mass (grams or kilograms).
Updated On: Jun 9, 2026
- \( 15.75 \times 10^{-3} \text{ g} \)
- \( 15.75 \text{ g} \)
- \( 252 \text{ g} \)
- \( 252 \times 10^{-3} \text{ g} \)
Show Solution
Verified By Collegedunia
The Correct Option is B
Solution and Explanation
Concept:
The heat required to raise the temperature of a mass of water is \( Q = mc\Delta T \). This heat must be supplied by the combustion of fuel: \( Q = m_{fuel} \times \text{Heat of Combustion} \).
Step 1: Calculate the heat required for the water.
Flow rate = 3.0 L/min = 3 kg/min (since density of water is 1 kg/L). Specific heat of water \( c = 4200 \text{ J kg}^{-1} \text{ K}^{-1} \). \( \Delta T = 77 - 27 = 50^\circ\text{C} = 50 \text{ K} \). $$ Q = 3 \text{ kg} \times 4200 \text{ J kg}^{-1} \text{ K}^{-1} \times 50 \text{ K} = 630,000 \text{ J/min} $$
Step 2: Determine the mass of fuel combusted.
$$ m_{fuel} = \frac{Q}{\text{Heat of Combustion}} = \frac{630,000}{4.0 \times 10^4} $$ $$ m_{fuel} = \frac{63}{4} = 15.75 \text{ g} $$ $$\boxed{15.75 \text{ g}}$$
Step 1: Calculate the heat required for the water.
Flow rate = 3.0 L/min = 3 kg/min (since density of water is 1 kg/L). Specific heat of water \( c = 4200 \text{ J kg}^{-1} \text{ K}^{-1} \). \( \Delta T = 77 - 27 = 50^\circ\text{C} = 50 \text{ K} \). $$ Q = 3 \text{ kg} \times 4200 \text{ J kg}^{-1} \text{ K}^{-1} \times 50 \text{ K} = 630,000 \text{ J/min} $$
Step 2: Determine the mass of fuel combusted.
$$ m_{fuel} = \frac{Q}{\text{Heat of Combustion}} = \frac{630,000}{4.0 \times 10^4} $$ $$ m_{fuel} = \frac{63}{4} = 15.75 \text{ g} $$ $$\boxed{15.75 \text{ g}}$$
Was this answer helpful?
0
0
Top AP EAPCET Physics Questions
- A body is projected from the ground at an angle of $\tan^{-1} \left( \frac{8}{7}\right)$ with the horizontal. The ratio of the maximum height attained by it to its range is
- A lens forms real and virtual images of an object, when the object is at $u_{1}$ and $u_{2}$ distances respectively. If the size of the virtual image is double that of the real image, then the focal length of the lens is (take, the magnification of the real image as $m$ )
- Two spheres $P$ and $Q$, each of mass $200\, g$ are attached to a string of length one metre as shown in the figure. The string and the spheres are then whirled in a horizontal circle about $O$ at a constant angular speed. The ratio of the tension in the string between $P$ and $Q$ to that of between $P$ and $O$ is $(P$ is at mid-point of the line joining $O$ and $Q$ )
- The radii of the two columns in a U - tube are r1 and r2. When a liquid of density p (angle of contact is $ 0{}^\circ $ ) is filled in it, the level difference of the liquid in the two arms is h. The surface tension of the liquid is: (g = acceleration due to gravity)
- A rigid metallic sphere is spinning around its own axis in the absence of external torque. If the temperature is raised, its volume increases by $9 \%$. The change in its angular speed is
View More Questions
Top AP EAPCET thermal properties of matter Questions
A 567 W bulb has a tungsten filament of length 40 cm and radius $\dfrac{2}{\pi}$ mm. If the radiation of the filament is 81% of that of a perfect black body, then the temperature of the filament is
(Stefan's constant, $\sigma = 5.67 \times 10^{-8}$ W m$^{-2}$ K$^{-4}$)- The part of the stress-strain curve where the Hooke's Law is valid is
- Two soap bubbles of radii \( r_1 \) and \( r_2 \) in vacuum coalesce isothermally to form a new bubble. The radius of the new soap bubble is
- One end of the steel rod is clamped to the roof and the other end is attached to a mass of 1000 kg as shown in the figure. The length of the rod is 50 cm and its cross-sectional area is 1000 mm$^2$. The change in the length of the rod due to the weight of the mass is \underline{\hspace{2cm}} .
- A circular film of a liquid has an area of 10 cm$^2$. If the work done in making its radius two times the initial radius is $8 \times 10^{-3$ J, the surface tension of the liquid is $\left(1+\frac{1}{a}\right)$ Nm$^{-1}$. The value of $a$ is}
View More Questions
Top AP EAPCET Questions
- A body is projected from the ground at an angle of $\tan^{-1} \left( \frac{8}{7}\right)$ with the horizontal. The ratio of the maximum height attained by it to its range is
- The four quantum numbers of the valence electron of potassium are :
- A lens forms real and virtual images of an object, when the object is at $u_{1}$ and $u_{2}$ distances respectively. If the size of the virtual image is double that of the real image, then the focal length of the lens is (take, the magnification of the real image as $m$ )
- Two spheres $P$ and $Q$, each of mass $200\, g$ are attached to a string of length one metre as shown in the figure. The string and the spheres are then whirled in a horizontal circle about $O$ at a constant angular speed. The ratio of the tension in the string between $P$ and $Q$ to that of between $P$ and $O$ is $(P$ is at mid-point of the line joining $O$ and $Q$ )
- The volume of $0.02\, M$ acidified permanganate solution required for complete reaction of $60\, mL$ of $0.01\, MI^{-}$ ion solution to form $I_2$ in $mL$ is
View More Questions