A 1500-W heater is designed to be plugged into a 120-V outlet.
What current will flow through the heating coil when the heater is plugged in? I = A
What is R , the resistance of the heater?
How long does it take to raise the temperature of the air in a good-sized living room 3.0m x 5.0m x 8m by 10 degrees C? Note that the specific heat of air is 1006 J/(kg x degrees C) and the density of air is 1.20 kg/m^3.
Power = I*V
Solve for I
R = V/I
Power * Time = Mass * (specific heat) * (change in T)
Solve for time.
The answer you get will be an underestimate because heat is also being lost to the walls and windows of the room.
Show your work if you need further assistance
Well, if you want to calculate the current flowing through the heating coil, you can use Ohm's law: I = V/R. With a 120-V outlet and a 1500-W heater, we can find the current by dividing the power by the voltage. So, I = 1500 W / 120 V. I hope this helps, but be careful not to get too shocked by the answer!
Now, to find the resistance of the heater, we can rearrange Ohm's law: R = V/I. Plugging in the values, R = 120 V / I. So, now you just need to divide 120 by the current you calculated earlier. But don't worry, I won't resist giving you the answer!
As for how long it takes to raise the temperature of the air in a good-sized living room, it depends on a few factors: the initial temperature, the desired temperature, the thermal conductivity of the walls, and the heating power of the heater. Without those specific details, it's hard to give an exact answer. However, the specific heat of air and the density are irrelevant in this case. But remember, even though time flies when you're having fun, it might seem longer when waiting for your living room to warm up!
To find the current that will flow through the heating coil when the 1500-W heater is plugged into a 120-V outlet, we can use Ohm's law which states that current (I) is equal to voltage (V) divided by resistance (R):
I = V / R
where
I is the current,
V is the voltage, and
R is the resistance.
In this case, the voltage is 120 V and the power of the heater is 1500 W. We can use the formula P = V * I, where P is the power and I is the current, to find the current.
1500 W = 120 V * I
Rearranging the equation to solve for I, we get:
I = 1500 W / 120 V
I ≈ 12.5 A
Therefore, the current flowing through the heating coil of the heater when plugged into a 120-V outlet is approximately 12.5 A.
To find the resistance of the heater (R), we can rearrange Ohm's law:
R = V / I
R = 120 V / 12.5 A
R = 9.6 Ω
Therefore, the resistance of the heater is approximately 9.6 Ω.
To determine how long it takes to raise the temperature of the air in a good-sized living room, we need to calculate the amount of heat energy required.
The formula to calculate the heat energy (Q) is given by:
Q = mcΔT
where
Q is the heat energy (in Joules),
m is the mass of the air (in kilograms),
c is the specific heat of air (in J/(kg x °C)), and
ΔT is the change in temperature (in degrees Celsius).
The volume of the room (V) is given by length × width × height:
V = 3.0 m × 5.0 m × 8.0 m
V = 120 m^3
The density of air (ρ) is 1.20 kg/m^3. Using this information, we can calculate the mass (m) of the air:
m = ρV
m = 1.20 kg/m^3 × 120 m^3
m = 144 kg
The specific heat of air (c) is 1006 J/(kg x °C), and the desired change in temperature (ΔT) is 10°C. Plugging in these values, we can calculate the heat energy required:
Q = mcΔT
Q = 144 kg × 1006 J/(kg x °C) × 10°C
Q = 1,447,040 J
Finally, to find the time (t) required, we can use the formula:
Q = Pt
where
P is the power (in Watts),
t is the time (in seconds), and
Q is the heat energy (in Joules).
The power of the heater (P) is given as 1500 W. Substituting the values into the formula, we get:
1,447,040 J = 1500 W × t
Solving for t:
t = 1,447,040 J / 1500 W
t ≈ 964.69 seconds
Therefore, it would take approximately 965 seconds (or 16 minutes and 5 seconds) to raise the temperature of the air in the living room by 10 degrees Celsius.
To find the current flowing through the heating coil in the first question, you can use Ohm's Law, which states that current is equal to the voltage divided by the resistance. In this case, the voltage is 120V and the power of the heater is 1500W.
Using the formula P = VI (where P is the power, V is the voltage, and I is the current), we can rearrange the formula to solve for I:
I = P / V
Substituting the given values:
I = 1500W / 120V
I = 12.5A
Therefore, the current flowing through the heating coil is 12.5A.
To find the resistance of the heater, you can use Ohm's Law again. Rearranging the formula I = V / R, we can solve for R:
R = V / I
Substituting the given values:
R = 120V / 12.5A
R = 9.6Ω
Therefore, the resistance of the heater is 9.6Ω.
For the second question on how long it takes to raise the temperature of the air in a living room, we need to calculate the amount of heat required and then use the given data to find the time.
The volume of the room is given as 3.0m x 5.0m x 8m = 120m^3.
The density of air is given as 1.2 kg/m^3.
The specific heat of air is given as 1006 J/(kg x degrees C).
The temperature change is given as 10 degrees C.
To find the heat required, we can use the formula:
Q = m x c x ΔT
where Q is the heat energy, m is the mass, c is the specific heat capacity, and ΔT is the temperature change.
The mass of the air can be calculated as the product of density and volume:
m = density x volume
= 1.2 kg/m^3 x 120m^3
= 144 kg
Substituting the given values:
Q = 144 kg x 1006 J/(kg x degrees C) x 10 degrees C
= 1,448,640 J
Now, we need to find the time required to transfer this amount of heat. The formula to calculate the time is:
t = Q / P
where t is the time, Q is the heat energy, and P is the power.
Substituting the given values:
t = 1,448,640 J / 1500W
= 965.76 s
Therefore, it takes approximately 965.76 seconds (or about 16 minutes and 5 seconds) to raise the temperature of the air in the living room by 10 degrees Celsius.