Solve each problem. Resistance of a WireThe resistance in ohms...

Question

Solve each problem. Resistance of a WireThe resistance in ohms of a platinum wire temperature sensor varies directly as the temperature in kelvins (K). If the resistance is 646 ohms at a temperature of 190 K, find the resistance at a temperature of 250 K.

Accepted Answer

Hey, everyone. Here, we are asked to use variation techniques to solve the following problem which is Gras Hoff's number. A dimensionless number used in quantifying heat transfer forces varies directly as the temperature in ranking R. If the temperature is 809 R, the Gras number evaluates to 19, 93. We are asked to calculate the value of Grasso's number. If the temperature is 1396 R, here we have four answer choice options. Answer A 34,327. Answer B 11,528 answer C 46,309 99 answer choice D 50,598. So here the key to solving this problem is to first set up an equation that represents our given statement. So we can first, before we begin setting up our equation, we first want to let G R be equal to or represent Grasso's Gras off's number. And then we want to let T sub R be equal to the temperature in ranking or R, the temperature in R. And then we need a proportionality constant. So we will let K be the proportionality constant. So again, K is our proportionality constant. And now we can set up our equation using our first statement here in our problem statement, which is that Grasso's number varies directly as the temperature in ranking. So this tells us that G R or the Grasso's number is equivalent to our proportionality constant K time times our temperature in ranking which is T sub R. So now we have found the equation that we need to use. So we want to start by finding the value of our proportionality constant. And we do this using our given information. So we are given the, the next part which is that the temperature when the temperature is nine R, that Grasso's number evaluates to 19,893. So we can just plug in these values since T sub R is in ranking and ranking is an absolute unit of temperature like Kelvin. So again, we can plug in these values. So we have 1009 or 19,893 Is equal to K, Our Proportionality Constant Times 809 R. So just solving for K, we see our proportionality constant K turns out to be approximately 24.5896 divided by R. So now that we have found our proportionality constant, we can calculate the value of Grasso number if the temperature is 1396 R. So just using our equation that we came up with and now substituting in our value for K and T sub R, we have G R or Grasso's number is equivalent to uh proportionality constant K which is 24.5896, divided by R times the temperature in ranking which is given as 1396 R. So now just multiplying these terms together, we see that grass number is, is going to be 34, And 27.08. And since we have a dimensionless number, the decimals don't really matter. So we can round this value to the nearest full number. So here we see that when the temperature is 1,396 R, that grasso's number is 34,327. So with this value that we have found and simplified, we are left with answer choice. A where again, Reso's number is 34,327. Thanks for watching. I hope you found this video helpful and I'll see you again next time.

Solve each problem. Resistance of a WireThe resistance in ohms of a platinum wire temperature sensor varies directly as the temperature in kelvins (K). If the resistance is 646 ohms at a temperature of 190 K, find the resistance at a temperature of 250 K.

Key Concepts

Direct Variation

Finding the Constant of Variation

Substitution and Solving Linear Equations

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