Thermal Properties of Matter

JEE Main level, numerical answer, medium

64 of 126

Question 64 of 126

A geyser heats water flowing at a rate of 2.0kg2.0kg per minute from 30∘C30^{\circ}C to 70∘C70^{\circ}C. If geyser operates on a gas burner, the rate of combustion of fuel will be _____ gmin⁡−1g{\min }^{-1}.
[Heat of combustion =8×103Jg−1=8\times {10}^{3}{Jg}^{-1}, Specific heat of water =4.2Jg−1C∘−1=4.2{Jg}^{-1}{C^{\circ}}^{-1}]

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Answer: 42

Given here, mass flow rate of water, dmdt=2kgmin⁡−1\dfrac{dm}{dt}=2kg{\min }^{-1}
The geyser heats the water, raising the temperature from θ1=30∘C{\theta }_{1}=30^{\circ}C to θ2=70∘C{\theta }_{2}=70^{\circ}C.
Total heat utilised in raising the temperature, ΔQΔt=dmdt×sΔθ\dfrac{\Delta Q}{\Delta t}=\dfrac{dm}{dt}\times s\Delta \theta
ΔQΔt=260×4.2×40=mt×L\dfrac{\Delta Q}{\Delta t}=\dfrac{2}{60}\times 4.2\times 40=\dfrac{m}{t}\times L
L=L= heat of combination=8×103Jg−1=8\times {10}^{3}J{g}^{-1}
Now, rate of consumption of fuel is mt=2×4.2×4060×8×103\dfrac{m}{t}=\dfrac{2\times 4.2\times 40}{60\times 8\times {10}^{3}}
=4.26×10−3=0.7×10−3kgsec⁡−1=\dfrac{4.2}{6}\times {10}^{-3}=0.7\times {10}^{-3}kg{\sec }^{-1}
=42gmin⁡−1=42g{\min }^{-1}

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