A brass rod 50.0 cm long expands 0.0734 cm when heated. Find the temperature change.
Using the equation Change in temp=change in length/original length * coefficient of linear expansion for brass I am getting the following result:
.0734 cm/(1.9x10^-5)(50 cm) = 193157.8947
Can anyone tell me what I'm doing wrong or how I convert my answer into Celsius degrees?
Thanks.
According to your formula, I get
∆T = ∆L/L * K
I assume that the coefficient is set up to produce °C or °K (which are really the same thing).
∆T = (.0734cm)/(50cm) * (1.9x10^-5) = 2.789x10^-8
Now, somehow that does not seem right. That would mean that K is just plain °C, which I doubt. Better check the formula, and the units on K, to see what else you need to include in the conversion.
To find the temperature change, you have correctly used the formula:
Change in temperature = (change in length / original length) * coefficient of linear expansion
However, it seems like you made a mistake in your calculation. Let's go through the correct calculation step by step:
Given:
Change in length = 0.0734 cm
Original length = 50.0 cm
Coefficient of linear expansion for brass = 1.9 x 10^-5 (1/°C)
Using the formula:
Change in temperature = (change in length / original length) * coefficient of linear expansion
Substituting the given values:
Change in temperature = (0.0734 cm / 50.0 cm) * (1.9 x 10^-5 1/°C)
Now we can calculate the temperature change:
Change in temperature = 0.001468 * (1.9 x 10^-5 1/°C)
Change in temperature = 2.788 x 10^-8 °C
So the temperature change is approximately 2.788 x 10^-8 °C.
Now, since the temperature change is very small in this case, it is usually more convenient to express it in Celsius (°C) rather than scientific notation. To convert the temperature change to Celsius, you can simply multiply it by 100 to move the decimal point two places to the right:
Temperature change in Celsius = (2.788 x 10^-8 °C) * 100
Temperature change in Celsius = 2.788 x 10^-6 °C
Therefore, the temperature change is approximately 2.788 x 10^-6 °C.
To find the temperature change, you made a slight mistake in your calculation. The correct formula for calculating the change in temperature is:
Change in temperature = (change in length) / (original length) / (coefficient of linear expansion for brass)
In this case, the original length is 50.0 cm, and the change in length is 0.0734 cm. The coefficient of linear expansion for brass varies depending on the type of brass, but it is typically around 1.9 x 10^-5 per degree Celsius.
Using the formula, the calculation would be:
Change in temperature = 0.0734 cm / (50.0 cm) / (1.9 x 10^-5 per degree Celsius)
Change in temperature = 0.0734 / (50.0 x 1.9 x 10^-5)
Change in temperature = 0.0734 / 0.000095
Change in temperature = 772.632 Celsius degrees
So, the correct change in temperature is approximately 772.632 degrees Celsius.