Name the THREE basic gas processes..

Original length ($L_0$) = 500 mm = 0.5 m
Elongation ($\Delta L$) = 0.25 mm = 0.00025 m

The strain is $\boxed{0.0005}$.

4.3.3 The Young modulus of the material.

Stress ($\sigma$) = 101.86 MPa = $101.86 \times 10^6$ Pa (from 4.3.1)
Strain ($\epsilon$) = 0.0005 (from 4.3.2)

The Young modulus of the material is $\boxed{203.72 \text{ GPa}}$.

QUESTION 5: HEAT

5.1 Name the THREE basic gas processes.

• Isobaric process (constant pressure)
• Isochoric process (constant volume)
• Isothermal process (constant temperature)

5.2 A square metal plate with sides 1 m long is at a temperature of 31 °C. There is a hole of 600 mm in diameter in the centre. The linear coefficient of expansion of the metal is $12.5 \times 10^{-6}$ /K.

5.2.1 Calculate: The temperature of the metal plate in if it is heated until the sides are 1,005 m long.

Initial length ($L_0$) = 1 m
Final length ($L_f$) = 1.005 m
Initial temperature ($T_0$) = 31 °C
Linear coefficient of expansion ($\alpha$) = $12.5 \times 10^{-6}$ /K

The formula for linear expansion is $\Delta L = \alpha L_0 \Delta T$.

The final temperature of the metal plate is $\boxed{431 \text{ °C}}$.

5.2.2 The diameter of the hole at this temperature.

Initial hole diameter ($D_0$) = 600 mm = 0.6 m
Linear coefficient of expansion ($\alpha$) = $12.5 \times 10^{-6}$ /K
Change in temperature ($\Delta T$) = 400 K (from 5.2.1)

The hole expands by the same linear expansion formula.

The diameter of the hole at this temperature is $\boxed{0.603 \text{ m}}$.

5.3 A cylinder has a capacity of 0,075 m$^3$ and is filled with oxygen at a pressure of 380 kPa and a temperature of 50 °C. Later it is found that owing to a leak, the pressure has dropped to 280 kPa and the temperature has decreased to 25 °C.

5.3.1 Calculate the mass of the oxygen that was initially in the cylinder if the gas constant is 265 J/kg.K.

Volume ($V$) = 0.075 m$^3$
Initial pressure ($P_1$) = 380 kPa = $380 \times 10^3$ Pa
Initial temperature ($T_1$) = 50 °C = $50 + 273.15 = 323.15$ K
Gas constant ($R$) = 265 J/kg.K

The ideal gas law is $PV = mRT$.

The mass of the oxygen initially in the cylinder is $\boxed{0.3328 \text{ kg}}$.