Water of volume 2 liter in a container is heated with a coil of 1 kw at 27^∘ C. The lid of the c

step 1 Hello students in the question is given that water of volume 2 liter volume is 2 liter in a cont

Water of volume 2 liter in a container is heated with a coil...

Water of volume 2 liter in a container is heated with a coil of $1 \mathrm{kw}$ at $27^{\circ} \mathrm{C}$. The lid of the container is open and energy dissipates at the rate of $160(\mathrm{~J} / \mathrm{S}) .$ In how much time temperature will rise from $27^{\circ} \mathrm{C}$ to $77^{\circ} \mathrm{C}$. Specific heat of water is $4.2\{(\mathrm{KJ}) /(\mathrm{Kg})\}$ (A) $7 \mathrm{~min}$ (B) $6 \min 2 \mathrm{~s}$ (C) $14 \mathrm{~min}$ (D) $8 \min 20 \mathrm{~S}$

Water of volume 2 liter in a container is heated with a coil of $1 \mathrm{kw}$ at $27^{\circ} \mathrm{C}$. The lid of the container is open and energy dissipates at the rate of $160(\mathrm{~J} / \mathrm{S}) .$ In how much time temperature will rise from $27^{\circ} \mathrm{C}$ to $77^{\circ} \mathrm{C}$. Specific heat of water is $4.2\{(\mathrm{KJ}) /(\mathrm{Kg})\}$
(A) $7 \mathrm{~min}$
(B) $6 \min 2 \mathrm{~s}$
(C) $14 \mathrm{~min}$
(D) $8 \min 20 \mathrm{~S}$

Key Concepts

Specific Heat Capacity

This is the amount of heat energy required to raise the temperature of a unit mass of a substance by one degree Celsius (or Kelvin). It is used in calculating the energy needed to change the temperature of a substance, using the formula Q = m × c × ?T, where m is mass, c is the specific heat capacity, and ?T is the change in temperature.

Energy Balance

In heating problems, the energy provided by a heat source must account for both the useful energy used to raise the temperature of the substance and any losses that occur during the process. Setting up the energy balance involves considering the net energy input after subtracting losses, which determines the rate of temperature rise.

Power, Energy, and Time Relationship

Power is defined as the rate at which energy is transferred or converted, and is measured in watts (joules per second). The relationship between power, energy, and time is given by the equation Energy = Power × Time, allowing one to calculate the time required for a given amount of energy transfer.

Heat Dissipation

This concept refers to the loss of energy from the system to the surroundings, often due to conduction, convection, or radiation. In open systems, some of the energy supplied to heat a substance is lost, reducing the effective energy available for raising the temperature, which must be accounted for in energy calculations.

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