thanks again to anyone who can possibly help!!!!! i wish i had a book or notes or something about this kind of stuff :(

The linear expansion coefficient of glass is 9 x 10^-6 (`C)^-1.

An automobile windshield has dimensions of 59 cm by 390 cm. What minimum spacing around the windshield is needed to prevent the windshield from breaking if the temp. changes to 146` F.?

Assume the normal temperature of the glass, when installed, is 66 F, so you want to design for an 80F rise in temperature. That is a 45 C temperature rise. The long dimension of the window will expand most, by an amount

390 cm * 45 C * 9*10^-6 C^-1 = 0.16 cm = 1.6 mm

You should leave a gap of 0.8 mm at each end. The gap at the top and bottom can be less, but might as well be the same.

A body cools from 50 degree celcious to 49 degree celcious in 5 seconds. How long will it take to cool from 40 degree celcious to 39 degree celcious? ( assume temperature of surroundings to be 30 degree celcious and newtons law of cooling is valid)

To solve this problem, we need to consider the linear expansion of the glass and calculate the minimum spacing around the windshield that will prevent it from breaking.

The linear expansion coefficient of glass is given as 9 x 10^-6 (`C)^-1. This means that for every 1 degree Celsius increase in temperature, the glass will expand by 9 x 10^-6 of its original size.

First, let's convert the given temperature from Fahrenheit to Celsius. The formula to convert Fahrenheit to Celsius is given by:

C = (F - 32) / 1.8

Plugging in the given temperature of 146` F, we have:

C = (146 - 32) / 1.8
C = 114 / 1.8
C = 63.33 `C

Now we can calculate the expansion of the glass using the linear expansion coefficient:

Expansion = Coefficient * Original Length * Change in Temperature

Here, the original length of the windshield is given as 390 cm. Therefore, the expansion is:

Expansion = (9 x 10^-6 `C)^-1 * 390 cm * 63.33 `C

Calculating this, we find:

Expansion = 0.000009 `C^-1 * 390 cm * 63.33 `C

Expansion = 0.0221016 cm

This means that the windshield will expand by approximately 0.0221016 cm due to the increase in temperature.

To prevent the windshield from breaking, we need to leave a minimum spacing around it to accommodate for this expansion. Therefore, the minimum spacing required would be slightly larger than the calculated expansion amount.

In this case, I would suggest adding a minimum spacing of 0.03 cm (or 0.03 cm) around the dimensions of the windshield to prevent breakage.

Note: It is always a good idea to consult a professional or refer to manufacturer specifications for specific details regarding the minimum spacing required for different materials and environmental conditions.