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QJEEM23Ch790c: JEE Main 2023 Chemistry - Class 11 JEEM23Ch790c Solution: When a electric heater is immersed in a gas for 100 s in a…

When a 60 W60 \mathrm{~W} electric heater is immersed in a gas for 100 s in a constant volume container with adiabatic walls, the temperature of the gas rises by 5∘C5^{\circ} \mathrm{C} . The heat capacity of the given gas is ___________ JK−1\mathrm{J} \mathrm{K}^{-1} (Nearest integer)

Step-by-Step Verified Solution

The heat provided by the heater is given by the equation:

Q=Power×TimeQ = \text{Power} \times \text{Time}

Substituting the given values:

Q=60 W×100 s=6000 JQ = 60 \, \text{W} \times 100 \, \text{s} = 6000 \, \text{J}

The heat capacity (C) is defined as the amount of heat required to raise the temperature of a substance by one degree. It is given by the equation:

C=Q/ΔTC = Q/\Delta T

Substituting the given values:

C=6000 J/5 °C=1200 J/KC = 6000 \, \text{J} / 5 \, \text{°C} = 1200 \, \text{J/K}

So, the heat capacity of the given gas is approximately 1200 J/K.

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