JEE Physics 2026 Question with Solution

Given: Water flows at $5.0 \, \text{L/min}$, its temperature increases from $27^\circ \text{C}$ to $87^\circ \text{C}$, specific heat capacity of water is $4200 \, \text{J/kg}\cdot{}^\circ\text{C}$, and heat of combustion of gas is $5.0 \times 10^4 \, \text{J/g}$.

Find: The mass rate of gas consumption in $\text{g/s}$.

By energy conservation, the rate of heat supplied by the gas equals the rate of heat absorbed by water.

Mass flow rate of water:

$$\dot{m}_{\text{water}} = 5.0 \, \frac{\text{L}}{\text{min}} \times \frac{1 \, \text{kg}}{1 \, \text{L}} \times \frac{1 \, \text{min}}{60 \, \text{s}} = \frac{5}{60} \, \frac{\text{kg}}{\text{s}} = \frac{1}{12} \, \frac{\text{kg}}{\text{s}}$$

Temperature rise:

$$\Delta T = 87^\circ \text{C} - 27^\circ \text{C} = 60^\circ \text{C}$$

Power absorbed by water:

$$P_{\text{water}} = \dot{m}_{\text{water}} \cdot s \cdot \Delta T$$ $$P_{\text{water}} = \left(\frac{1}{12}\right) \times 4200 \times 60 = 21000 \, \text{J/s}$$

Let the gas consumption rate be $\dot{m}_{\text{gas}}$ in $\text{g/s}$. Then

$$P_{\text{gas}} = \dot{m}_{\text{gas}} \times 5.0 \times 10^4$$

Using $P_{\text{gas}} = P_{\text{water}}$,

$$\dot{m}_{\text{gas}} \times 50000 = 21000$$ $$\dot{m}_{\text{gas}} = \frac{21000}{50000} = 0.42 \, \text{g/s}$$

Therefore, the rate of consumption of gas is $0.42 \, \text{g/s}$. The correct option is C.

Given: The specific heat is in $\text{J/kg}\cdot{}^\circ\text{C}$ while the heat of combustion is in $\text{J/g}$.

Find: A consistent way to compare the two energy rates.

The important step is to keep units consistent. Water flow is first converted into $\text{kg/s}$ because the specific heat is given per kilogram, while gas consumption is left in $\text{g/s}$ because the combustion value is given per gram.

Once the heat absorbed per second by water is found as $21000 \, \text{J/s}$, dividing by $5.0 \times 10^4 \, \text{J/g}$ directly gives the gas consumption in $\text{g/s}$.

Thus,

$$\dot{m}_{\text{gas}} = \frac{21000}{5.0 \times 10^4} = 0.42 \, \text{g/s}$$

Hence, the correct option is C.