A thermal cap used in certain apparatus consist of silica rod which fits tightly inside an aluminium tube whose internal diameter is 8mm at 0 degree c … elcius. Calculate what change in temperature to produce channel whose cross section equal to 1 mm

change in temperature is a decrease by 268.734 K

Explanation:

We are given;

Temperature: T1 = 0°C = 273 K

Internal diameter; d1 = 8mm

Final diameter; d2 = 1 mm

To solve this, we will use Charles law formula since pressure is constant.

Thus;

V1/T1 = V2/T2

Where T2 is the final temperature.

Now, V1 and V2 are volume

Volume is given by: V = area x height

We are told the cross section is equal except for the diameter.

Thus;

V1 = A1 × h

V2 = A2 × h

Thus;

(A1 × h)/T1 = (A2 × h)/T2

h will cancel out and making T2 the subject, we have;

T2 = (A2 × T1)/A1

A2 = π(d2)²/4

A1 = π(d1)²/4

Thus;

T2 = [(π(d2)²/4) × T1]/(π(d1)²/4)

π and 4 will cancel out to givw;

T2 = ((d2)²× T1)/(d1)²

T2 = (1² × 273)/8²

T2 = 273/64

T2 = 4.266 K

Thus;

Change in temperature = T2 - T1 = 4.266 - 273 = -268.734 K

Thus, change in temperature is a decrease by 268.734 K