Answer to Question #129407 in Physics for Darlington

Question

A heating coil of resistance 20 ohms connected to a 200v source is used to boil a certain quantity of water in a container of heat capacity 100JK¹ for 2 minutes. of the initial temperature of the water is 40⁰c. Calculate th mass of the water on the container. (Specific heat capacity of water=4.2*10³Kg¹k¹, assume boiling point of watet=100⁰c)

Answer 1

According to the Joule–Lenz law, the energy delivered to the system from the coil is:

$$Q_{in} = \dfrac{U^2}{R}t$$

where $U = 200V$, $R = 20\space Ohms$ and $t = 2min = 120s$.

Thus, obtain:

$$Q_{in} = \dfrac{200^2}{20}\cdot 120 = 2.4\times 10^{5}J$$

The equation of the thermal balance will be:

$$Q_{in} = C_{container}\Delta T + c_{water}m_{water}\Delta T$$

where $C_{container} = 100J/K$ is the heat capacity of the container, $c_{water} = 4.2\times 10^3 J/kg\cdot K$ is the specific heat capacity of water, $\Delta T = 100\degree C-40\degree C = 60\degree C = 60 K$ is the temperature difference and $m_{water}$ is the mass of water.

Expressing $m_{water}$ from the last equation, obtain:

$$m_{water} = \dfrac{Q_{in} - C_{container}\Delta T}{c_{water}\Delta T} = \dfrac{2.4\times 10^5 - 100\cdot 60}{4.2\times 10^3\cdot 60} \approx 0.929 kg$$

Answer. 0.929 kg.