Question

In: Physics

A) A 232.0 g piece of lead is heated to 84.0oC and then dropped into a...

A) A 232.0 g piece of lead is heated to 84.0^oC and then dropped into a calorimeter containing 514.0 g of water that initally is at 25.0^oC. Neglecting the heat capacity of the container, find the final equilibrium temperature (in ^oC) of the lead and water.

B) A small spinning asteroid is in a circular orbit around a star, much like the earth's motion around our sun. The asteroid has a surface area of 8.30 m². The total power it absorbs from the star is 4400 W. Assuming the surface is an ideal absorber and radiator, calculate the equilibrium temperature of the asteroid (in K).

C) An ideal monatomic gas goes from P₁ = 190 atm and V₁ = 50 m³ to P₂ and V₂ via an adiabatic process. If P₂= 30 atm, what is V₂ in m³?

Solutions

Expert Solution

Given

mass of lead piece = 232 g = 0.232 kg

mass of water in calorimeter = 514g = 0.514 kg

Initial temperature of water = 25^oc

Initial temperature of lead piece = 84^oc

we know heat capacity of lead and water are 125.60J/kgand

4.184 kJ/kg-k

Conserving energy

heat lost by lead=heat gained by water

m_Lc_L(T_L- T)= m_wc_w (T - T_w)

0.232*125.604(84-T) = 0.514*4.184*1000(T - 25)

29.140128*(84 -T) = 2150.576*(T - 25)

2447.77075 – 29.140128*T= 2150.576*T - 53764.4

56212.1708 = 2179.71613*T

T = 25.78^o C

---------------------------------------------

ideal absorber/radiator, means it will radiate according to

E=A*sigma*T⁴

where E is the energy emitted/sec,

A is the surface area of the emitting object,

sigma is a constant the Stefan Boltzman's constant = 5.67x10^-8 W/m²/K⁴

T is the radiating temperature in degrees Kelvin

perfect radiators absorb all the energy incident upon them and then radiate all that energy to space

4400 J/s (1W=1J/s), we have

4400W = 8.3m² x 5.67x10^-8 W/m²/K⁴ *T⁴

T⁴=4400W/(8.3m² x 5.67x10^-8W/m²/K⁴)

T⁴=9.349 x 10⁹ K⁴

T=310.95K

T = 310 K

---------------------------------------------

Data:

V1 = 50 m³

P1 = 190 atm

P2 = 30 atm

Use P*V^k = constant.

The value of k is 5/3 for a monatomic gas

P₁*V₁^k = P₂*V₂^k

Solve for V₂:

P₁*V₁^k/P₂ = V₂^k

190*50^5/3/30 = V₂^5/3

V2 = 151.33 m³

genius_generous answered 1 year ago

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