An electric heater the temperature of 120g of water in a thin light vessel through 10k in 2 minutes, when placed in 70g of water contained in a metal vessel of mass 0.55kg the temperature rises through 9k in the same time. Calculate from the above
The heat supplied in 2 minutes by d heater
The power of the heater
Well, isn't that a heated situation we have here! Let's break it down and crunch some numbers.
First, let's calculate the heat supplied by the heater in 2 minutes. To do that, we need to use the formula:
Q = mcΔT
For the first scenario with the light vessel and 120g of water, we have:
Q1 = (120g)(4.18 J/g°C)(10K)
And for the second scenario with the metal vessel and 70g of water, we have:
Q2 = (70g)(4.18 J/g°C)(9K)
Now, let's turn up the heat on those calculations:
Q1 = 5016J
Q2 = 2646.6J
So, the heat supplied by the heater in 2 minutes for the first scenario is 5016J, and for the second scenario, it's 2646.6J.
Now, let's move on to the power of the heater. Power is defined as the rate at which work is done or energy is transferred, and it's given by the formula:
P = ΔQ/Δt
Since we're given the time (2 minutes), we can plug in our values:
P1 = 5016J/120s
P2 = 2646.6J/120s
Calculating those spicy numbers:
P1 ≈ 41.8W
P2 ≈ 22.1W
Therefore, the power of the heater in the first scenario is approximately 41.8W, and in the second scenario, it's about 22.1W.
Now, hold on tight, because things just got heated in here!
To find the heat supplied in 2 minutes by the electric heater, we can use the formula:
Heat = mass x specific heat capacity x temperature change
For the first scenario with 120g of water, the temperature change is 10K. We know that the specific heat capacity of water is approximately 4.18 J/g°C.
Heat = 120g x 4.18 J/g°C x 10K
Heat = 5016 J
Therefore, the heat supplied in 2 minutes by the heater is 5016 J.
To calculate the power of the heater, we can use the formula:
Power = Heat / time
Time in this case is 2 minutes, which is equal to 120 seconds.
Power = 5016 J / 120 s
Power ≈ 41.8 W
Therefore, the power of the heater is approximately 41.8 Watts.
To calculate the heat supplied by the heater in 2 minutes, we can use the formula:
Q = mcΔT
Where:
Q is the heat supplied
m is the mass of the substance
c is the specific heat capacity of the substance
ΔT is the change in temperature
For the first scenario with 120g of water, the mass (m) is 120g = 0.120kg, and the change in temperature (ΔT) is 10K.
The specific heat capacity for water (c) is approximately 4200 J/kg·K.
Using the formula, we can calculate the heat supplied:
Q = (0.120kg) * (4200 J/kg·K) * (10K)
Q = 50,400 J
Therefore, the heat supplied by the heater in 2 minutes for the first scenario is 50,400 Joules.
To find the power of the heater, we can use the formula:
Power = Energy/Time
In this case, the energy is the heat supplied (Q) and the time is 2 minutes, which needs to be converted to seconds.
Given that 1 minute is 60 seconds, the total time in seconds is 2 minutes * 60 seconds/minute = 120 seconds.
So, the power of the heater can be calculated as:
Power = 50,400 J / 120 s
Power = 420 W
Therefore, the power of the heater is 420 Watts.