Question

1. How much heat is required 200 mL of ice at - 22 degrees Celsius (at typical Freezer temperature).
2. One mole of a monoatomic perfect gas initially at temperature T₀ expands From volume V₀ to 2V₀ (a) at constant temperature, (b) at constant pressure. Calculate the work of expansion and the heat absorbed by the gas in each case.
3. Determine the mass and specific volume of argon gas in a vessel at 150 kPa and 20 degrees Celsius. The vessel is spherical and has a radius of 5m.
4. A container which has a volume 0.1 m³ is fitted with plunger enclosing 0.5 kg of steam at 0.4 MPa. Calculate the amount of heat transferred and the work done when the steam is heated to 300 degrees Celsius at constant pressure.

Answer 1

Question 1 is unclear

Question 2

$ΔU= \frac{3}{2} ​ P(V_{2} ​ −V _{1} ​ )$

$= \frac{3}{2} ​ P(2V_{0} ​ −V _{0} ​ )= \frac{3}{2} ​ PV _{0} ​ = \frac{3}{2} ​ RT _{0}​$

$W=P(V _{2} ​ −V _{0} ​ )=PV_{0} ​ =RT _{0} ​$

$\therefore Q= \frac{3}{2} ​ RT ​ +RT_{o} ​ = \frac{5}{2} ​ RT _{0} ​$

Question 3

specific volume = $\frac{Volume}{mass}$

Specific volume =$\frac{R \cdot T } {P}$

where

R = ideal gas constant =  8.314 J mol⁻¹ K⁻¹

T= temperature = 20 + 273 = 293 K

P = pressure = 150kPa = 150000 Pa

Specific volume $=\frac{8.314 × 293 } {150000} ​$

specific volume = 0.016 m³ kg^-1

Mass = $\frac{volume}{s.volume}$

volume = $\frac{4}{3}πr^{3} = \frac{4}{3}π5^{3} = 523.8 m^{3}$

mass = $\frac{523.8}{0.016} = 32737.5 kg$

Question 4

Amount of heat = mcΔθ

m= mass = 0.5kg

c= specific heat capacity of steam = 2110 J/Kg•K

Δθ = 300 - 100 = 200 degree Celsius

Amount of heat = 0.5 × 2110 × 100 = 105500J

Work done = PΔV

P= pressure = 0.4 MPa = 400000Pa

ΔV = 0.15 - 0.10 = 0.05

$\frac{V_1}{T_1} = \frac{V_2}{T_2}$

$\frac{0.10}{373} = \frac{V_2}{573}$

V₂ = 0.15

Work done = 400000 × 0.05 = 20000J