the resistance of a platinum resistance thermometer is 200.0 ohm at o degree centigrade and 257.6 ohm when immersed in hot bath,what is the temperature of the bath when 'alpha' for platinum is 0.00392degree centigrade inverse.
R2 = R1 + 0.00392(T2-T1)R1 = 257.6 Ohms.
200 + 0.00392(T2-0)200 = 257.6
200 + 0.784(T2-0) = 257.6
200 + 0.784T2 = 257.6
0.784T2 = 57.6
T2 = 73.5o C.
Well, it looks like we have a Fahrenheit 257.6 situation here! But seriously, let's calculate the temperature of the bath.
The formula we can use here is:
Rt = Ro * (1 + α * ΔT)
Where:
Rt is the resistance at the given temperature T,
Ro is the resistance at 0 degrees Celsius,
α is the temperature coefficient for platinum, and
ΔT is the change in temperature between 0 degrees Celsius and T.
Given that the resistance at 0 degrees Celsius is 200.0 ohms, and the resistance at the hot bath is 257.6 ohms, we can rearrange the formula to solve for ΔT:
ΔT = (Rt - Ro) / (Ro * α)
Plugging in the values:
ΔT = (257.6 - 200.0) / (200.0 * 0.00392)
Calculating that, we find:
ΔT ≈ 14.897
So, the temperature of the hot bath, when the coefficient alpha for platinum is 0.00392 degree Celsius inverse, is approximately 14.897 degrees Celsius. Now, go enjoy a nice soothing bath!
To find the temperature of the hot bath, we can use the formula for the change in resistance of the platinum resistance thermometer:
ΔR = R2 - R1
Where:
ΔR is the change in resistance
R2 is the resistance at the temperature of the hot bath
R1 is the resistance at 0 degrees Celsius
Given:
R1 = 200.0 ohm
R2 = 257.6 ohm
α (alpha) = 0.00392 1/°C
Substituting the given values into the formula, we have:
ΔR = 257.6 ohm - 200.0 ohm
ΔR = 57.6 ohm
Now, we can use the formula for the change in resistance as a function of temperature:
ΔR = α * R1 * ΔT
Where:
ΔT is the change in temperature
α is the temperature coefficient of resistance
Rearranging the formula to solve for ΔT, we have:
ΔT = ΔR / (α * R1)
Substituting the values into the formula, we have:
ΔT = 57.6 ohm / (0.00392 1/°C * 200.0 ohm)
Calculating the value, we find:
ΔT ≈ 73.47 °C
Finally, to find the temperature of the hot bath, we add ΔT to the initial temperature (0 °C):
Temperature of the hot bath = 0 °C + 73.47 °C
Therefore, the temperature of the hot bath is approximately 73.47 °C.
To determine the temperature of the bath using the resistance values of the platinum resistance thermometer, we can utilize the relationship between resistance and temperature, which is given by the equation:
R = R₀ * (1 + α * t)
Where:
R is the resistance at a given temperature
R₀ is the resistance at the reference temperature (0 degrees Celsius, in this case)
α is the temperature coefficient of resistance for platinum (0.00392 degree Celsius inverse)
t is the change in temperature from the reference temperature
First, we need to find the change in temperature (t) from the reference temperature to the temperature of the hot bath.
Let's substitute the given resistance values into the equation:
200.0 Ω = R₀ * (1 + α * 0) --> Equation 1 (at 0 degrees Celsius)
257.6 Ω = R₀ * (1 + α * t) --> Equation 2 (at the temperature of the bath)
Dividing Equation 2 by Equation 1, we get:
257.6 Ω / 200.0 Ω = (R₀ * (1 + α * t)) / (R₀ * (1 + α * 0))
Simplifying the equation further:
1.288 = 1 + α * t
Next, rearrange the equation to isolate the change in temperature (t):
α * t = 1.288 - 1
α * t = 0.288
Finally, divide both sides by α to solve for t:
t = 0.288 / α
Now, substitute the value of α (0.00392 degree Celsius inverse) into the equation:
t = 0.288 / 0.00392
Calculating the result:
t ≈ 73.47 degrees Celsius
Therefore, the temperature of the bath is approximately 73.47 degrees Celsius.