area temperature pressure

Question

7.3 A steel plate with dimensions 80 cm x 40 cm x 20 cm is placed in an electrical furnace. The steel plate is heated from 37 °C to 410 °C. The coefficient of linear expansion on the steel plate is 19 x 10 -6 1°C. Calculate the following: 7.3.1 The expansion in the length of the plate in cm 7.3.2 The area at the temperature of 410 deg. Celsius of the 80 cm x 40 cm side in mm2 7.3.3 The increase in volume in m3 7.4 The volume of a gas is 0,493 M3 at 73 °C and a pressure of 740 kPa. Calculate the thermodynamic temperature of the gas if the volume is 0,0749 m3 at a pressure of 1 300 kPa.

Answer 1

(7.3.1)

The dimensions of the steel plate = 80cm*40cm*20cm.

Initial Temperature is 37°C

Final Temperature is 410°C

Coefficient of the linear expansion is 19*10^-6

We know that

dl = 80 * 19*10^-6(410-37)

dl = 0.5669

Expansion in the length of steel plate is 0.5669 cm.

Answer 2

(7.3.2)

The dimensions of the steel plate = 80cm*40cm.

Initial Temperature is 37°C

Final Temperature is 410°C

Area of the steel plate = l*b

A0 = 80 * 40

Area A0 = 3200

Coefficient of the linear expansion is 19*10^-6

Co-efficient of the Area expansion = 2*(Coefficient of the linear expansion)

β = 2α

β = 2*19*10^-6

β = 38*10^-6

Co-efficient of the Area expansion = 38*10^-6.

We know that

Area  of the steel plate at 410°C is 3245.35 cm².

Answer 3

(7.3.3)

The dimensions of the steel plate = 80cm*40cm*20cm.

Initial Temperature is 37°C

Final Temperature is 410°C

Volume of the steel plate = lbh

V0 = 80 * 40 * 20

Volume V0 = 64000 cm³

Coefficient of the linear expansion is 19*10^-6

Co-efficient of the Area expansion = 3*(Coefficient of the linear expansion)

γ = 3α

γ = 3*19*10^-6

γ = 57*10^-6

Co-efficient of the Area expansion = 57*10^-6.

We know that

Change in the volume of the steel plate is 1360.7 cm³. 

Answer 4

(7.4)

The volume of the gas = 0.493 m³.

Pressure of the gas = 740 kPa

Temperature of the gas = 73°C = 73+273 = 346 K

The volume of the gas at Temperature T2 is 0.0749 m³

The Pressure of the gas at Temperature T2 is 1300 kPa.

From the Equation of the ideal gas

T2 = 92.3 K

T2 = 92.3 - 273

T2 = -180.6°C

The Temperature of the gas = -180.6°C.