A heating coil of resistance 20 Ω connected to a 220V source is use to boil a certain quantity of water in a container of heat capacity 100Jkg^-1K^-1 for 2mins. If the initial temperature of the water is 40oC, calculate the mass of the water in the container. (specific heat capacity of water = 4.2x 10^3 kg^-1 J^-1 K ^-1 assume boiling point of water = 100oC).
Answers
Explanation:
A heating coil of resistance 20 Ω connected to a 220V source is use to boil a certain quantity of water in a container of heat capacity 100Jkg^-1K^-1 for 2mins. If the initial temperature of the water is 40oC, calculate the mass of the water in the container. (specific heat capacity of water = 4.2x 10^3 kg^-1 J^-1 K ^-1 assume boiling point of water = 100oC).
Answer:
Explanation:
To calculate the mass of water in the calorimeter, we will first find the heat energy supplied by the heating coil and then use the specific heat capacity of water to find the mass of the water.
Calculate the power of the heating coil:
The power (P) is given by the formula P = V^2 / R, where V is the voltage and R is the resistance.
P = (220 V)^2 / 20 Ω
P = 48400 / 20
P = 2420 W
Calculate the heat energy supplied by the heating coil:
The heat energy (Q) supplied by the heating coil is given by the formula Q = P * t, where t is the time in seconds.
t = 2 minutes * 60 seconds/minute = 120 seconds
Q = 2420 W * 120 s
Q = 290400 J
Calculate the temperature difference:
ΔT = T_final - T_initial
ΔT = 100°C - 40°C
ΔT = 60°C
Calculate the mass of the water:
We know that the heat energy is also given by the formula Q = m * C * ΔT, where m is the mass of the water, C is the specific heat capacity of water (Cw), and ΔT is the temperature difference.
Rearranging the formula to solve for the mass of water:
m = Q / (C * ΔT)
m = 290400 J / (4200 J/(kg·K) * 60 K)
m = 290400 J / 252000 J/kg
m ≈ 1.15 kg
Therefore, the mass of the water in the calorimeter is approximately 1.15 kg.