JEE Mains 31-Jan-2023 Shift 2 Solved Paper

The amount of heat energy required to raise the temperature of a substance can be calculated as:
Q=m×c×∆T
where Q is the heat energy required, m is the mass of the substance, c is its specific heat capacity, and ∆T is the change in temperature.
The time required to heat a substance can be calculated as :
t=‌

Q

P

where t is the time required, and P is the power of the heating device.
The actual power output of the heating device can be calculated as:
P‌actual ‌=P‌input ‌×‌ efficiency ‌
where P−input is the input power to the device and efficiency is the fraction of input power that is actually converted to useful power output.
Substituting the given values:
Q=2‌kg×4200J∕kg∕K×(60−10)=2‌kg×4200J∕kg∕K×50K=4200×50×2J=420,000J
P‌input ‌=2000W=2000J∕ s
P‌actual ‌=2000×0.7=1400J∕ s
t=‌

Q

P‌actual ‌

=‌

420,000

1400

J∕ s=300 s
So, the time required to heat 2‌kg of water from 10∘C to 60∘C is approximately 300 s.