A geyser, operating on LPG (liquefied petroleum gas) heats...

A geyser, operating on LPG (liquefied petroleum gas) heats water flowing at the rate of $3.0$ litres per minutes, from $27^{\circ} \mathrm{C}$ to $77^{\circ} \mathrm{C}$. If the heat of combustion of LPG is $40,000 \mathrm{~J} / \mathrm{g}$, how much fuel, in $\mathrm{g}$, is consumed per minute? (Specific heat capacity of water is $4200 \mathrm{~J} / \mathrm{kg}-\mathrm{K}$ ) (a) $15.25$ (b) $15.50$ (c) $15.75$ (d) $16.00$

Key Concepts

Heat of Combustion

Heat of combustion is the amount of heat released when a specified amount of a fuel undergoes complete combustion. This concept is crucial in energy calculations involving fuel consumption, as it provides the link between the fuel’s mass and the total energy it can generate upon burning.

Energy Transfer

Energy transfer involves the movement of energy from one system or object to another. In thermal processes, this transfer is often in the form of heat, and understanding the involved energy transfer is essential for quantifying how much energy is required to achieve a specific temperature change in a substance.

Temperature Change

Temperature change refers to the difference between the final and initial temperatures of a substance. It is a critical factor in determining the amount of heat energy required to raise or lower the temperature of that substance, as the energy needed is directly proportional to the change in temperature.

Specific Heat Capacity

Specific heat capacity is a property of a material that indicates the amount of energy required to raise the temperature of a unit mass of the substance by one degree Celsius (or one Kelvin). This concept is fundamental when calculating the energy needed for temperature changes in various substances.

Mass Flow Rate

Mass flow rate is the quantity of mass passing through a given surface or point per unit time. In thermal systems, it is used to determine how much substance is being heated or cooled over a period, which in turn affects the total energy transfer calculations.

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