A pressurized 2-m-diameter tank of water has a 10-cm-diameter orifice at the bottom where water discharges to the atmosphere. Th

Answer:

Volume change percentage is 2.60%

Water level increase is 4.138 mm

Explanation:

Provided data

Water volume V = 500 L

Initial temperature T1 = 20°C

Final temperature T2 = 80°C

Diameter of the vat = 2 m

Objective

We aim to determine percentage change in volume and the rise in water level.

Solution

We will apply the bulk modulus equation, which relates the change in pressure to the change in volume.

It can similarly relate to density changes.

Thus,

E = ................1

And ............2

Here, ρ denotes density. The density at 20°C = 998 kg/m³.

The density at 80°C = 972 kg/m³.

Plugging in these values into equation 2 gives

dV = 0.0130 m³

Therefore, the percentage change in volume will be

dV % =  × 100

dV % =  × 100

dV % = 2.60 %

Hence, the percentage change in volume is 2.60%

Initial volume v1 = ................3

Final volume v2 = ................4

From equations 3 and 4, subtract v1 from v2.

v2 - v1 =  

dV =

Substituting all values yields

0.0130 =

Thus, dl = 0.004138 m.

Consequently, the water level rises by 4.138 mm.

Answer:

a. 25! = (Approximately)

b. 24!

Explanation:

a. In a Playfair cipher, there are 25 keys available because it is structured in a 5 * 4 grid. By using permutations to enumerate all potential configurations, we derive: 25! = 1.551121004×10²⁵ =

Although there are 26 letters available, in the Playfair cipher, the letters 'i' and 'j' are treated as a single letter.

b. Considering any configuration of 5x5, each of the four row shifts yields equivalent configurations, amounting to five total equivalencies. Similarly, for each of these five setups, any of the four column shifts also results in equivalent arrangements. Therefore, each configuration corresponds to 25 equivalent arrangements. Consequently, the total count of distinct keys can be expressed as:

25!/25 = 24! = 6.204484017×10²³