MATH PHYS WOULD YOU MIND HELPINB ME ON THESE QUESTIONS

001) 233.15 K

002) 3. a difference of 9 on the Fahrenheit scale.

003) 0.0153 m

004) 9.9×10⁷ N/m²

005) 0.199 cm

006) 3.07 m

007) 24.8 psi

Explanation:

001

Converting Fahrenheit to Celsius:

T(°F) = 1.8 T(°C) + 32

The temperature at which they are numerically equal is:

T = 1.8 T + 32

-0.8T = 32

T = -40

-40°F is the same temperature as -40°C, which in Kelvins is:

T = -40°C + 273.15

T = 233.15 K

002

Kelvins scale equally with Celsius:

ΔT(K) = ΔT(°C)

Fahrenheit scales 1.8 times with Celsius, and therefore with Kelvins:

ΔT(°F) = 1.8 ΔT(°C) = 1.8 ΔT(K)

If ΔT(K) = 5 K, then:

ΔT(°C) = ΔT(K) = 5°C

ΔT(°F) = 1.8 ΔT(K) = 9°F

003

Linear thermal expansion is:

ΔL = L α ΔT

where ΔL is the change in length,

L is the original length,

α is the linear expansion coefficient,

and ΔT is the change in temperature.

Plugging in values:

ΔL = (31 m) (11×10⁻⁶ (°C)⁻¹) (40°C − (-5°C))

ΔL = 0.0153 m

004

Thermal stress is:

σ = E α ΔT

where E is Young's modulus.

Plugging in values:

σ = (20×10¹⁰ N/m²) (11×10⁻⁶ (°C)⁻¹) (40°C − (-5°C))

σ = 9.9×10⁷ N/m²

005

Volumetric thermal expansion is:

ΔV = V β ΔT

where ΔV is the change in volume,

V is the original volume,

β is the volumetric expansion coefficient,

and ΔT is the change in temperature.

The change in volume is:

ΔV = A Δh

ΔV = π r² Δh

ΔV = π (d/2)² Δh

ΔV = 1/4 π d² Δh

The volume of the bulb is:

V = 4/3 π r³

V = 4/3 π (D/2)³

V = 1/6 π D³

Substituting:

1/4 π d² Δh = 1/6 π D³ β ΔT

1/4 d² Δh = 1/6 D³ β ΔT

3 d² Δh = 2 D³ β ΔT

Assuming the diameter of the capillary tube is 0.0059 cm, and the diameter of the bulb is 0.12 cm, then:

3 (0.0059 cm)² Δh = 2 (0.12 cm)³ (0.000182 (°C)⁻¹) (33°C)

Δh = 0.199 cm

006

If each beam is 140 m, then the length they increase by is:

ΔL = L α ΔT

ΔL = (140 m) (1.2×10⁻⁵ (°C)⁻¹) (20°C)

ΔL = 0.0336 m

So the length of each beam increases to 140.0336 m.  Using Pythagorean theorem to find the height:

(140.0336 m)² = (140 m)² + y²

y = 3.07 m

007

Use the ideal gas law:

PV = nRT

where P is the absolute pressure,

V is the volume,

n is the number of moles,

R is the gas constant,

and T is the absolute temperature.

Since V, n, and R are constant:

P₁ / T₁ = P₂ / T₂

Plugging in values:

(22 psi + 14.7 psi) / (0.17 + 273.15 K) = (P + 14.7 psi) / (21 + 273.15 K)

P = 24.8 psi

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